Can a Ryzen 3950x be air-cooled with a budget, tower air cooler?

[amolang]

It seems AMD recommend water-cooling it,
But any tower cooler (from Gammaxx to Noctua) can air-cool it without overclocking?

[Omega]

A $50 air cooler performs just as well as a $150 liquid cooler.

AMD recommends liquid cooling because these chips are small and produce a lot of heat, because they are so small the heatspreader doesn't have a lot of surface area to absorb the heat in. So it's best to get the heat away from the chip immediately using liquid.

You can cool that chip just fine with a high-end air cooler.

And don't consider buying the 3950x for gaming, it delivers the same gaming performance as the 3600 and up.

[r.linder]

At stock, not really, from my experience with the 3900X. The automatic boost that all Ryzen CPUs use works against Ryzen 9 in terms of cooling, as the voltages are going all the way to 1.5v under load, resulting in considerably higher temperatures despite the clocks being far too low for that voltage.

I have my 3900X overclocked per CCX as more BIOS revisions support that now (they brought that in because of that Worktool program that did it before, only now there should be no risk)
At the moment, I have CCX1 set to 4.55, 2 set to 4.45, 3 set to 4.35, and 4 set to 4.25 (3 cores per CCX with the 12 core 3900X) at 1.38v. Performance is decently improved over stock and PBO, while temperatures are around 10 degrees lower than stock because the voltages aren't skyrocketing to their maximum under load constantly, as the voltage is actually set.
Even then, my maximum temperature in P95 small FFT was 87.5 C, while stock was instantly throttling, and that's with a Corsair H115i RGB Platinum with the pump at its maximum. SMT is also off, as that adds a few degrees and hinders gaming performance half of the time.

That being said, as Omega stated, the 3950X isn't a good value for gaming because it's barely an improvement over the 3900X, which isn't a real improvement over Ryzen 7 and 5, typically within less than 10~15 FPS at best, and the 9700K beats it in gaming. So for gaming with Ryzen 3000, you don't need more than a 3600 for solely gaming or 3700X for streaming+gaming without overspending.