This may be misunderstanding the function of PoW. Bitcoin PoW provides three things: selection, security, and incentive. The compute resource burn is an externality, although, it also ends up providing an important function, economic distribution. For PoW to work,it has to be hard to produce, easy to verify, and most importantly, attest to one and only one state of the blockchain. The last part is where this fails as…
This isn't true. There are an infinite number of inputs that result in the same solution for bitcoin (or any hash)