I have little knowledge about crypto mining architectures, but what I do know is that most proof of work algorithms are based on the extensive evaluation of hash functions, which are inherently digital, as most are based on bitwise operations. The advantage of ASICS is they possess custom hardware instructions to compute these hash functions faster.

I, therefore, believe there is little sense in trying to do it by analog means, as the whole thing is inherently based on digital concepts. It could be possible, though, to develop other proof of work algorithms that are based on analog concepts and, hence, could be solved using analog computers, as you call them.

This has two flaws, however. First, the idea of proof of work is to be hard. If you could solve a proof of work problem easily, it wouldn't work as proof that you spent work trying to solve it :x. Second, in order for a crypto system to be accessible and decentralized, it needs to be easily adopted by people. If one is developed with the requirement of some special analog system, it would lose its accessibility right of the bat.