That's only mathematically true. The advantage is way too small to be relevant.
Your advantage is having exhausted a fraction of the search space. But that fraction is tiny.
You're trying to find a hash with a value below a certain threshold (simplified said, a hash starting with a certain amount of zeroes). You do this by trying random inputs to the hash function. Every input has the same probability of getting an output that is low enough in value. You are not advancing by having tried other inputs. It's practically equivalent to rolling multiple dices until enough of them show a one. Every roll has the same probability of succeeding regardless of the rolls before.
That's the whole question: is it relevant or not? Even if it makes mining slightly more profitable, that's a win. No need to remind you that those who mine do it exclusively for profit.
It's not. Your advancement is that of exhausting a part of the search space of SHA256 inputs for a given output. We would be in deep trouble if you made any significant advancements there or even got close to it by multiple orders of magnitude off.
> We would be in deep trouble if you made any significant advancements there
Not necessarily. The whole idea is that it maybe more profitable to withhold a block for some time. "More profitable" means that you make more money at the end. Not that you make billions in a second.
I'm not commenting on the Bitcoin economics, but on the specific problem of a partial hash inversion which Bitcoin uses. If any amount of compute you can bring up would grant you any significant amount of information about the likelihood of a (partial) hash inversion for an untested input in your search space by means of having searched a significant amount of the search space, SHA256 would be broken.
In hopefully simpler words; You want to find a hash with all zeroes. So you start trying inputs from your search space and hash them to see if they match that criterion. Every single input you try has the same probability of matching. After trying a lot of inputs you have exhausted a part of the search space. You have already tried many incorrect inputs. At some point if you keep only trying incorrect inputs you should have exhausted the whole search space and the last remaining possible input has to be the correct one resulting in an all zeroes hash. So the probability of the next hash being the correct one should go up during your search as you learn information about the remaining candidates in the search space. If this information is in any way significant in practice with any feasible amount of computing power, the cryptographic hash function is insecure. Of course with Bitcoin you aren't searching for a full hash inversion with all zeroes but only for a partial one starting with some zeroes, but that does not change the fundamentals. It should be infeasible to learn any significant information about the output of untried inputs by trying other inputs.
If SHA256 was to be broken in that way, we'd be in big trouble and Bitcoin would be the least of our worries.
I think you are missing something very basic here: the longer you compute, the higher the likelihood that you will find the hash before the others.
The extreme case being that if you can try ALL the possibilities before the others can start, then you are guarantee to find the solution before them.