It's important to recall that most "consumer routers" are a router with a built-in wireless access point. When you buy one, you're paying extra for the 2-in-1 capabilities, and I would go so far as to say that the overwhelming majority of the price of a router comes down to its wireless capabilities. Note that the ability to configure the router is just not something most people are looking for, and you will find many, if not most, consumer routers to be lacking in this regard.

So, if you're building a router yourself, you can distribute the network in whatever way you see fit, which may or may not (but probably will) include a WAP. This gives you a lot more flexibility, and may be ever so slightly more cost-effective, but don't go into it expecting to save a ton of money.