Suppose a coin switches its hashing algorithm each time a new block is found. Also suppose that new algorithm itself is randomly generated, and the previous block contains the instructions on how to perform it.

Would that coin be ASIC-proof?

I understand that if there are  X different algorithms, miners can still buy X different types of ASICs (one for each algorithm). But if X is large, or even unlimited, it seems completely infeasible to have specialized equipment?