I think another way to think about it is to allow 'long planning' queries. I.e. where it is allowed to spend a second, or maybe a few seconds choosing the best plan. That may involve collecting more statistics or running a query for a little bit.
There'd be a few hurdles to get over before we could get such a feature. The planner currently has a habit of making changes to the parsed query, so we'd either need to not do that, or make a copy of it before modifying it. The former would be best.
For instance, if you have a left join (and let's say it can't use an index for whatever reason) - the optimal plan will probably be different if almost every row has a matching row(s) in the join table than if only a few do.