It would also put viewers in a bubble where they're unwilling to look at a site with opposing viewpoints because they'd have to pay more. It's similar to the purported drawbacks of the Facebook Zero/Internet.org initiative
1. Human psyche isn't amenable to looking at things disagreeing with them. Any system evolved / used by humans will have that problem. Even without internet.org / zero / facebook / lots of paid websites - most people live in their own bubble.
2. Even without internet.org/zero - facebook already puts you into your own bubble. Things similar to those you like are shown more. There is no dislike button for similar deliberate purposes. Facebook blames this on users, but they know that showing you things that you like is a good way to keep you coming back for more.
3. In effect you are saying paid websites would "put viewers in a bubble where they're unwilling to look at a site with opposing viewpoints", whereas without the paid websites they are already in the same bubble. I don't see a difference.