Powerful router or access points Why don't we use more powerful routers that have better signal reception instead of adding access points to the network?

I'm not sure I really understand the question, but I think you are confused. Why would routers have better signal reception that WAPs?

A router with Wi-Fi capability merely has a WAP added to it.

WAPs may be placed where you wouldn't place a router (e.g., in the ceiling in the middles of a room), moving the WAP closer to the clients. Multiple WAPs can all be on the same LAN, allowing roaming without reauthentication.