you wouldn’t be “freezing” anything. Each possible combination of input tokens maps to one output probability distribution. Those values are fixed and they are what they are whether you compute them or not, or when, or how many times.

Now you can either precompute the whole table (theory), or somehow compute each cell value every time you need it (practice). In either case, the resulting function (table lookup vs matrix multiplications) takes in only the context, and produces a probability distribution. And the mapping they generate is the same for all possible inputs. So they are the same function. A function can be implemented in multiple ways, but the implementation is not the function itself. The only difference between the two in this case is the implementation, or more specifically, whether you precompute a table or not. But the function itself is the same.

You are somehow saying that your choice of implementation for that function will somehow change the function. Which means that according to you, if you do precompute (or possibly cache, full precomputation is just an infinite cache size) individual mappings it somehow magically makes some magic happen that gains some deep insight. It does not. We have already established that it is the same function.