By caching templates, it shouldn't be forgotten that they could contain dynamic or randomly generated content, so it should be possible for parser functions to disable the cache, of course this must be done recursively then. I am not sure whether this is the case already, I just recall Extension:Variables behaving buggy on cached templates and when I last checked I think there already was some way for preventing caching but it didn't really work... Guess I will look into this again soon.

The reason the template expansion cache is only for invocations with empty arguments is just the difficulty of the implementation. I left it for later.

A naive implementation would involve traversing the whole tree under the <part> in order to generate a hash for fetching the expansion. That's O(N) in the node count, and if you had nested arguments, it becomes O(N^2) in the string length. It's a design goal to avoid such O(N^2) cases. So it's necessary to store subtree hashes in each of the node objects, which complicates construction slightly.