Even an external access point presents a single point of failure.
Lose your AP and a good chunk of your users will be offline or inconvenienced, just as they would be if the card in the router died.
If the router dies, an external AP doesnt really help you anyway.
Think of it in different terms, its a single point of administration, and easier to install. Ship the box to the site preconfigured, and even the ditzy receptionist can get it up and running.
In the case either device dies, you have more to worry about than any individual component.
If you really want to avoid outages, then you need to invest in a full 1+1 setup, redundant routers with redundant WAN circuits, redundant switches, APs and controllers.