Re-running searches (sending a POST request again) can be more CPU/IO intensive than rearranging existing results on the fly. Is this something only SMF can help us with or can bitcointalk do something about it?
You should try using ninjastic.space website when you want to search for something in forum, it is giving very good results and it is usually much faster.
I guess someone could make another patch to improve forum search, but it is never going to be good enough.