(like pillows, computer mice, and sleep masks)
You skip a distinction between two types of "durable goods", which seems relevant here: Whether the item would seem icky or benign to acquire secondhand.
Everybody draws that line in a different place, but I'd propose that pillows and sleep masks (and headphone earcups, underwear, shoes) very commonly fall on the "eww" side of the line: You wouldn't want to get the item secondhand, and/or the amount of cleaning it would take to render a secondhand one of the item clean enough to not gross you out would destroy the item.
I wouldn't mind a secondhand pillowcase, because I can launder it on hot and dry it in the sun and be content that it's as clean as anything I could buy new, possibly cleaner. But a secondhand pillow seems unpleasant; I don't want to be sticking my face in all the dust and dander that's gotten into it from other peoples' houses, and laundering most pillows causes their filling to mat up and spoils their texture.
I wouldn't mind a secondhand computer mouse, because if it looks icky I can wipe it down with water or some cleaner on all the parts of it that I actually touch. But if I was getting a secondhand pair of over-ear headphones, I would want to replace the ear and headband padding (or at least launder it if it was designed to survive that) because rubbing a stranger's skin and hair oils on myself like that would just be gross.
Similarly, I'm happy to thrift or inherit solid wood furniture, but I'm extremely reluctant to accept secondhand upholstered items, because you can't really wash upholstery and who knows what's living in it.
For items in the "ok with getting it secondhand" category, your scheme would work, but so would buying a secondhand version of the target item, keeping it if you like it, and selling it along at a price almost identical to what you paid for it if you don't like it. This trades a little more hassle for a lot more control of when you get the item, and it is likely cheaper to buy and resell several of the item than to pay 2x the cost of new. Sure, you only get to try a used one, but only the first person in your scheme gets to try the item new anyway.
For items in the "not ok with getting it secondhand" category, your scheme does not seem very tenable. Maybe you could choose an order of trying things based on how used an item each individual is willing to tolerate, and balance the prices for it based on how used the items are by the time they reach each participant? You could potentially use disposable covers over the parts that would be unhygenic without them, but that adds a lot of complexity and trust that the other people won't be gross with the item.
The usual way to try several of items you wouldn't want secondhand is to travel to some brick-and-mortar stores and examine new instances of the item you're considering. The showroom format for items like mattresses and pillows creates a strong social pressure to not interact with the display items in a way that would render them "used" (such as getting bodily fluids on a mattress or pillow). This pressure to keep items pristine, and subsequent trust that the item being tried has been kept in a situation with that pressure, would be hard to replicate in the scenario of letting people try the item at home.
Another logistical constraint to the idea of shipping stuff from home to home is simply storage space. How many people do you know live in a house or apartment large enough to easily store a few dozen extras of a particular "durable good" for the time it'd take them to test them all?
I would be very interested in seeing a price breakdown comparing doing a scheme like yours by mail against doing it with a series of regional showrooms. I've been shopping for a new vacuum cleaner and wishing that there was some format of event for such small appliances where people who love theirs would bring them in and let others try them. Maybe the manufacturers could be involved, either in promising to replace items broken by the event, or giving some small incentive to users whose participation causes others to purchase from that brand. I wouldn't trust such a showcase held by any individual manufacturer, but a community organized one using a combination of items donated (or loaned) by brands and items purchased by the group from brands unwilling to donate would help buyers make more informed decisions and discover their own preferences.
A dozen regional showrooms of this type could showcase a dozen different types of item, and rotate what items are shown where each month.
This looks very non-robust. What stops the second person from keeping it all? They only paid 1/n, after all. And shipping it all to the third person is such a pain. Also, they might've broken or used up or lost or had a cat chew on the cables of one thing. It would make more sense for the first person to pay for it themselves, and then each person pay the previous person for whatever they have. The consolidated collection is worth more than the parts individually, so it's still valuable even after being used. The first person to kick off the item-donation circle has to put capital at risk, of course, but one could use a dominant assurance contract to pool capital to buy it for them.
The capitalism version of this is to just buy each item you want to try and sell it on Craigslist if you don't like it. Then the overhead is nx*(Craigslist penalty). For most products the Craigslist penalty hovers around 0.5, but for some it can be significantly higher and you can sell them almost for the new price.
Possible improvement: people are unlikely to be maximally idiosyncratic, and we don't necessarily need to find the best product, only one that is good enough.
Products are likely distributed such that there's a cluster of products that most people dislike and a cluster of products that are good enough for most people and only a few in the middle where individual preference make a big difference.
Given this, we should be able to cut the search short in a variety of ways. We still get all n products initially, but can quickly rule out the worst ones and pick the best ones quickly. Rather than send all n to the first person, since 1 product to each person. Then they rotate. After a product has been rejected or accepted k or m times, where we have to work out what k and m are based on the underlying quality distribution of the products (we may have to guess at this) and how confident we want to be we got a good enough choice for everyone, then we can just pick one of the options that crosses the m threshold whether we tried it or not.
Hopefully that makes sense. Not sure I explained all the details precisely enough to not leave some room for error.
You could probably make a business doing this, and hopefully that would make n very large (although presumably people won't wait forever so you will probably want multiple sets of products). You could also let people keep whichever product they like best and return the rest (and then you replace their favorite).
You can sort-of already do this by just buying all of the products yourself and returning all of them you don't like, although that hurts your favorite business since they usually can't sell returns for full price. Making this "how the business works" should help customers (since they won't fell bad about trying all of them) and hopefully the business too (since it will be known that most of the products are used and that's ok).
A problem when trying to purchase some classes of products (like pillows, computer mice, and sleep masks) is that it is difficult to sample lots of them first-hand before making a purchase. This forces one to rely on product reviews or to settle for one's limited experience (such as just buying the same kind that a friend has that seems good enough, or trying the few available samples at a brick and mortar store).
Here is a naive scheme to allow a group of people to sample a bunch of kinds of a single product before making a purchase:
At the end of the scheme, each of the people will have their favorite product, for an average cost equal to twice the average cost of the products, plus shipping costs. (There's some subtlety here where, e.g. if better products tend to be more expensive, then you would expect people to pay more than the average.)
The above scheme can be improved in simple ways, such as not throwing away the products used during the sampling process, and instead letting people keep them (and then somehow distributing the savings). The more diverse people's tastes are, the higher the savings. The contender products can also be chosen in "smart" ways such as by reading product reviews online (not adding such a preliminary research step would be silly, since it would just be emulating what brick and mortar stores already do). If more than people are found, the overhead can also be reduced (with people, products, and an average cost of products, the expected cost will be , plus shipping).
Some things I like about this scheme:
The main disadvantage seems to be the difficulty of coordinating to find a bunch of people who are all interested in buying the same kind of product, and then managing all the logistics. The scheme also doesn't work for consumables, disposable goods, and experiences. Large items like mattresses may also have shipping costs that are too high.
Some questions I have:
Thanks to Vipul Naik for reading a draft of this post and suggesting an improvement.