This wouldn't personally affect me (at least not most of the time). However, a design choice like this is just not a smart thing unless they bundle internet with every console (which is frankly absurd). I know plenty of people who play offline so they wouldn't be able to get the next Xbox. And it would essentially be only semi-viable in first world countries.
As of right now though I still won't be putting too much faith into this rumor. Especially when the plethora of no used games rumors pretty much turned out to be false (via Gamestop's article).