You're conflating two things and dismissing the functionality being asked for as "already there" misses the point. Acting as a wifi repeater, or acting as a router with a wifi-connected WAN-side link is supported (as it is on essentially every AP). The problem with doing that is both WiFi links have to run on the same channels. You, best-case scenario, cut speeds in half. In "real world" scenarios, it's usually close to 2/3 slower. The reason you use an external USB WiFi adapter is because the two separate chipsets can run on different channels, and clients on the private side of the network will see the full bandwidth available as if they were connected directly to the external AP.
It's especially important for travel routers, as it is uncommon to be in a place where you can use an ethernet connection for the WAN side. Losing half the bandwidth or more can move a hotel network from "usable" to "unusable".