There's a lot of myth that's developed around thermal paste, mostly made up by the companies who want to sell you more paste.
The vast majority of the heat transfer from the CPU to heat sink is via metal on metal contact. You can in fact run the CPU without any thermal paste. It'll run a bit hotter than with paste, but it'll run just fine. It won't blow up. It won't instantly throttle. (Yes this video is of an older CPU, but one that had a reputation for running even hotter than modern CPUs.)
https://www.youtube.com/watch?v=RAr2wKZ_nes
The only purpose of the paste is to fill in microscopic air gaps that form between the CPU's heat spreader and heat sink because both surfaces are not perfectly flat. Nothing more. It is not intended to be the primary heat transfer medium. Paste is about 100x worse at heat transfer than metal on metal; we only use it because it's about 100x better than air. In other words, if you have enough paste on there for there to be air bubbles in the paste, you have too much paste. If you have a layer of paste between the two metal surfaces like mayonnaise on a sandwich, you've got too much paste and it'll run hotter than if you had no paste. Paste is not magic. Almost anything gooey enough to fill in air gaps and conducts heat better than air will work. People have even used toothpaste as a temporary measure (I wouldn't recommend it because it contains abrasives).
As long as the paste is still gooey and contaminants like dirt, dust, or hair hasn't fallen into it, it's fine to re-use it. Contaminants are killer because they prevent the two metal surfaces from contacting, meaning all your heat transfer is through the paste. I put the heatsink on, and squish it around until I feel metal starting to grind on metal (indicating I've squeezed out all excess paste), then strap it down.