"GDP is more of a measure of economic activity than value". I think this a very good intuition.
As I understand it, a main source of confusion in discussions like this stems from mixing up the notion of "value" as (A) price*quantity=revenue and (B) the difference between the consumer's willingness to pay and the price.
"A" is what counts towards GDP -- mostly for practical reasons, since prices and quantities are, at least theoretically, are straightforward to measure on a national level. However, this definition goes against the intuition of lots of people, who usually think of value as something like the idea in definition "B".
My rephrasing of it would go something like this: (1) nowadays very powerful transistors can be had for a few cents, (2) we know that people did pay a lot of money for inferior devices in the past, (3) therefore we are very rich today (at least measured in transistors-speed-per-cent), which leads to the not totally unfounded conclusion (4): GDP is a poor measure of "value" or "national wealth" in the sense of definition "B".
This is by and large true as long as you accept definition B -- which, in turn, turns out to be the (textbook) definition of consumer surplus. Which is something that was never intended to be captured by GDP -- mostly, because consumer surplus is just very complex to measure: it is very hard to estimate how much people would be willing to pay for certain items (and how much would be sold at those prices; basically, you are trying to estimate a demand curve).
Quantifying the gain from new products is a sub-sub-field of empirical industrial organization in itself: Petrin's 2002 seminal paper that tries to do it for the market of minivans (titled, funnily enough "Quantifying the Benefits of New Products: The Case of the Minivan") is still compulsory reading in graduate IO courses. But, as you can tell from the granularity and specificity of the topic, it looks hopeless to perform these exercises for the entirety of the economy, every year. So we work what we have, which is GDP.