It can work. It works much better if there are no obstructions in the beam path - using a reflector or other beam-concentrating antenna does not make "the problems with trees and buildings in the way" go away.
I have played around with this just using a stainless steel bowl as a crude reflector. For actual deployments, I use real antennas built from the ground up for the purpose; so the closest I've gotten to repurposing a satellite dish would be that stainless steel bowl.
Small hint towards success - separate the concepts of "router" and "WiFi access point" in your mind. Very common to conflate them. Also helps you miss most of the gear that will do the sort of job you want to do here, which are the latter, not the former. Nothing about the function of a router has anything to do with WiFi, other than low-end consumer gear putting the two in one box.