He will be fine. Should he update his CPU? Of course, he'd get better frame timing and lower latency with better general performance, but for all intents and purposes, it's just fine for modern gaming.
The 3060 (Especially the ti) is capable of 1440p 16:9 gaming with 60fps or higher if you play anything not super modern. And even modern games, just push the settings down - with DLSS, FSR, or raw resolution scaling if the game only has that. Hell, use either one's built in scaling options and those work wonders, too. I used the 5700xt (2600x CPU) on a 21:9 1440 monitor and got 60fps+ in a lot of games without scaling, and minor scaling helped tremendously (going upwards of 90 - 100 fps in a lot of more recent games). 5700 xt is similarly powerful as the 3060, so I see no reason why it couldn't do the same. The TI, obviously, would without any doubt. Even with his CPU. Don't lie to the poor person, lol.
3070 can do scaling 4k, natively if it's an older game. 3070 TI / 3080+ can do 4k natively more often, or a much higher scaler. 3080 TI+ is best for native 4k. Of course this is all moot when you talk about older games, as even the 3060 can do 4k on things from 4/5 years ago. As for the 3060 and 4K - he's not actually wrong. A lot of modern games can run on that kind of card 4k / 24-30 FPS. They said acceptable, not recommended.
And for your 3080: That sounds really weird. I run 32:9 1440p with a 3080, and that tends to run 60 FPS just fine.