> Why not simplify by removing parameters from the URL altogether?

Caching. Put a caching proxy in front of your api endpoint and enjoy.

This is the same reason you'll want to do:

    /api/customer/1234/order/abcd

instead of:

    /api?customer=1234&order=abcd

Because even if your cache includes query strings (which it may, and you can configure it to), you lose order. Now you also have to configure your cache to ignore ordering on the query string, and that's a lot less obvious (and probably not even HTTP compliant?).