For crypto mining, the speed of computation before the next block was mined was the constraint so GPUs were being used for parallel computation before ASIC miners were built. This is a great example of where ASICs shine: deterministic simple algorithms that don't require much if any I/O.

LLMs have a minimum RAM requirement in order to even load the model so even if you built a dedicated LLM card with an ASIC, you would still need at least that amount of RAM on the card. You'd probably want more RAM in order to store context because that takes RAM as well. At that point you pretty much have a GPU with an ASIC instead of more general compute units and no video outputs.

You might get some improvements by using an ASIC for LLMs but not nearly as much as when ASICs started being used for mining.

They're actually not because they have randomness built in. Since we are working with probabilities, it won't always pick the next token that has the highest probability and the randomness can be tuned via a "temperature" setting to make it more or less likely that it will choose the most probable token.

The weights for the model could be stored in a firmware chip but you still need RAM because it pulls all the weights into RAM in order to perform the calculations.