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There is always going to be some subjectiveness to it - but few are going to buy a 3060/70 class card with the intention of playing the latest and greatest games at 4K with quality setting which compliment that. Sure they can play older games or newer ones at reduced quality setting at 4K but it is always a relative position - it isn't about the exceptions.
Well it kinda is, because if I google some 3070 benchmarks and look at performance in a sample of modern AAA games it performs quite nicely at 4k in almost everything. So you have to go to exceptions to claim otherwise. I just looked at Tomsharware 15 game average for a quick average across a wide array of modern games (in 4k Ultra), and the 3070FE is 61.2FPS average.
I'm not particularly trying to defend the 3070 as "a 4k card", I've never made that claim. But to the degree it's not, you have to pretty much go to exceptions with it, it's not the rule even if you ignore the vast swath of games on the market that aren't demanding AAA games and you narrowly focus apriori on the one that are, you still only see a small fraction of them struggle and even then struggle is by a trivial amount. If you look at steam stats of games played, they list the top 100, I just took those peak numbers put them in a spreadsheet and the top 10 games account for 55% of the peak players. Everything in the top 10 a 3070 can play in 4k easily. And even of the entire top 100 games there's probably only a couple it'd struggle with, Cyberpunk, Maybe Ark because it's so horribly optimized.
It's a problem with interpretation of modern bench marking. Using a suite of all the latest and greatest games is good for stress testing different hardware against each other to see relative speeds, but it's NOT representative of what people play. Most sane people aren't going to spend hard earned money on buying more expensive hardware to eliminate a few exceptions which they might not even play! It's why a standard of a few exceptions prevent a card being "4k" has almost zero real utility. Like when I bought my 3080, I saw there were exceptions in games like MS FS2020, 4k Ultra isn't possible and it was kind of a standalone game in that regard, but I don't even play FS2020 and never will, so what? Nor will most people for that matter. it's a misleading and useless metric, only if you condition it in some sensible way can you really make it useful.