Our current academical journals are horrible. On the one hand charge a lot of money for access to their papers. On the other hand the fail to uphold the research standards they endorse.
The New England Journal of Medicine for example has endorsed the CONSORT guidelines on best practice in trial reporting. When Ben Goldacre sent him a letter about how out of 23 papers Ben Goldacre analysed only 3 were completely in accord with the CONSORT guidelines, they weren't even willing to print the letter.
The CONSORT guidelines don't require that researchers do fancy statistics instead of using p-values but just require basics like a paper explicitly mentioning when it reports outcomes that weren't preregistered. If the journal would care about high scientific standards it wouldn't be a big deal to uphold the CONSORT guidelines. Unfortunately, the other top medical journals aren't much better.
Why is it hard to establish a new journal that has higher standards? As Yudkowsky writes in Moloch's toolbox that academics have to publish in journals of high prestige and journals happens to be in high prestige when high quality papers are submitted to them. It's a chicken-and-egg problem.
How could we start a new journal that would get scientists willing to submit papers to the journal? If the journal would pay every author of a paper $50,000 for publishing the paper scientists would have an incentive to publish in the journal.
Even if the money alone isn't enough to warrant the scientist to publish in a no-name journal, the journal would soon stop being a no-name journal because scientists would expect that their colleges want to publish in the journal to get the money. That expectation makes the journal more prestigious. The expectations that other people expect the journal to get more prestigious in-turn will increase it's prestige.
Funding this Journal of High Standards wouldn't be a cheap project, but the money that payed to the scientists who publish the papers isn't going to waste. It's like giving a grant to the scientist expect that when you give them the grant you usually ask them what they want to do with the grant money and in this system they can decide for themselves what they are going to do with the money.
It would be a bit like XPrizes but instead of giving the scientists specific goals, it's "Do something worthwhile and then write a high quality paper about it".