As dumb as it sounds, it is probably easier that way. Sometimes in LANs it is easier to get data out then back in. For example, a lot of dorm networks don't support Chromecast devices because chromecasts tries to multicast on the LAN for discovery, but dorms have networking policies that prevent this.

A webcam that sends the data out to the internet then back would avoid the discovery issue by using an external webserver as a rendezvous point.

I don't think people spend a lot of time thinking about their home networking. You could imagine most people just plug in their home routers and it is a crapshoot whether or not the router will support the necessary functionality, whereas a router will always enable communication to the outside world (or people would return it ASAP).

With that said, this seems like a straightforward technical problem that may have technical solutions.