Whats to stop these bots from just stealing from bitcoin in every wallet thats been dormant for a few months/years in the same way they do with these puzzles?
Every extra bit doubles the effort for a bot. The entropy of like 69-bits is pretty low and can be solved within a few seconds.
70-bits doubles that, 71-bits double the 70-bit's effort and so on. The effort grows exponentially.
So if the entropy is 256-bit, that's way too much effort for a bot to solve within timely manner.
That’s not totally accurate, every bit does not double the complexity but multiplies it by sqrt(2). This is due to how the algorithm operates.
Edit : if you know the public key of the wallet