if somebody gives me a single device that's both a modem and a router, why would one need the other router?
You don't, unless the "other" router has some special features that you want that the service provider's modem/router does not provide.
If you don't mind setting up all new wireless connections for each of your wireless devices with the Actiontec device, you can probably simplify things a bit by having one device perform both modem and router duties.
But everything comes with a downside as well. With a combination modem/router device.....if the modem in the device has a problem, then you must replace the router as well...and set up new connections for all your devices again.
Or, if the router has a problem, you have to replace the modem as well and go through the setup with your service provider again to get online.