In the UK at least, they mostly do. You park up, plug the car in, tap your contactless card and that starts the charge. Once the charge completes (or you unplug the car), the charger works out how much electricity you used and your card gets charged accordingly. In my experience there aren't too many charging points that don't accept contactless payments in this way.
Sometimes having memberships, RFID cards or apps for the different charging networks unlocks cheaper rates though, so contactless payments don't always end up being the most economical in the long run and that can make it harder to compare charging providers, hence why things like Zap-Map and Electroverse were born.
Sometimes having memberships, RFID cards or apps for the different charging networks unlocks cheaper rates though, so contactless payments don't always end up being the most economical in the long run and that can make it harder to compare charging providers, hence why things like Zap-Map and Electroverse were born.