- does the planner take previous runs of the same query and it's execution time into account? If not, why?
No, because that isn't how it works. And while I'm no planner expert I'm not imagining any particularly compelling argument for why it would even make sense to try. The book-keeping would be expensive and dealing with supposedly an ever-changing dataset would in many cases make any such comparisons be meaningless.
- assuming the query to be immutable, would it be possible for the planner to microbenchmark a few different plans instead of trying to estimate the cost? As in, actually executing the query with different plans and caching the best one.
No, the planner may not cause execution. While I could imagine extending EXPLAIN to somehow retrieve and maybe even try alternative plans that have been fully constructed today I'm not holding my breath.
There is little reason for the project to give any real weight to "assuming the query to be immutable". We do want to fix the planner to behave better if it is mis-behaving, otherwise you do have access to cost parameters, and potentially other planner toggles if you've truly run into an intractable problem.
