Stock cooler is 1000000% adequate for a locked CPU and will not compromise performance or really acoustics much if you tune the fan correctly in the BIOS.
I never assumed they'd have to. Intel boxes its processors assuming that everyone who buys one is opening a PC for the first time. The last thing they want to do is spend thousands replacing CPUs for people who don't know what thermal paste is in the interest of not spending a few cents pre-applying some.
No. Absolutely no. Kryonaut is spectacular if you're delidding. If you're not, it's a spectacular waste of money. Putting aside shit-tier outliers like the stuff you get 50g of from China for $1.99, the difference in practical use between the best thermal pastes and the worst is consistently found to be less than 5C, usually less than 3C. Spending $14 on 1g of Kryonaut when you can get 4g of MX-4 for half the price is completely unnecessary, and telling others to do so is spreading terrible misinformation.
Unless you're delidding. Then Kryonaut away, but liquid metal pastes are a better idea there.