AMD rates it as non-turbo usage, ex: my $200 3600 is 65W TDP, has a package limit of 88W, and is designed to reach 65W without turboing; if I manually set the package limit to 65W, all cores will sit at the base clock of 3.6GHz forever. 88W hard package limit will be enforced under overclocking unless overridden by user.
The comparison is the $250 9600k, same single-threaded performance, 3600 is roughly 30% faster in multi-threaded; 95W TDP, soft package limit of 150W, and will exceed that under some situations under stock, and will absolutely exceed it overclocked.
So, Intel, in this case, costs 25% more, has 30% less performance, has 46% more TDP, and 70% more actual maximum usage... and to add insult to injury, AMD's stock cooler is beefier than Intel's: I believe AMD's stock cooler can sink 88W, I do not believe the Intel one can manage 150W+.
As you said, Intel's stock coolers are known for being loud, aren't actually too great at dissipating heat, and aren't even included on higher TDP chips. So you're almost automatically spending an extra $20+ over the chip price on a decent cooler.
On the other hand, AMD ships solid coolers with (pretty much?) every chip. I've run my R5 1600 with the stock cooler for two ish years without any real heat or noise issues.
In the case of Intel, the claimed TDP is a fairy tale.
[1]: https://www.youtube.com/watch?v=6u4ew6IT4Vo