If they were going to separate tiers of play by proficiency bonus increase they would have done it back when they released 5e. It was the absolute most natural way to do those breakdowns but they chose to not do it that way.
And the reason for that break wasn't the proficiency bonus I suspect - I think it was spell slots. Levels 5-10 gets you up to level 5 spells and no higher - and I think that's the determiner for where that second tier ends and where the next tier starts. At level 11 the full casters get to start casting 6th level spells - and 6th level spells are where the special rules on spellcasting start to come into play. Sorcerers only get to use spell points to buy up to 5th level slots, spell progression is basically one 6+ slot per level from 11-20, etc.
I think that the expectation is that the thing that differentiates "high level play" from "mid level play" is the casters getting access to 6th level spells. That's where a lot of folks feel their games start to change. Getting an extra +1 to proficiency bonus isn't actually enough of a change to the power level to change the feel of the game, but unlocking those higher level spells definitely can be depending on the group.
yeah, about mechanics of 6th level spells that are only available to full casters I agree, but 6th level spell really are not that special.
3rd level is a big boost in power and 5th level spells. 7th level spells are bigger jump from 6th that 6th level are from 5th level.
So, yeah, new tier should be at 3rd level spells, 5th level spells, 7th level spells
and finally 9th level spells.
I'm a bit late in replying to these posts, but this is a part of 5e's design that's really interesting to me.
The convention that everybody gets power spikes at the change of tier levels--5th, 11th, and 17th--felt really elegant to me since I read about it in a blog back at the beginning of 5e's life cycle (can't for the life of me remember where, sadly). For 5th level it works great; fly, fireball, spirit guardians, and conjure animals are huge, and they pair excellently with all the fight-y classes getting extra attack. For 17th level it works about as well as everything else at high levels (barbarians get an extra damage die on crits and a 6th rage. What?!?)--but it clearly makes sense for 17th level to be the last cut point.
11th level is weird, though. Most fight-y types get a solid power spike, with some ranger and monk subclasses being a bit iffy. And, as @Jer points out, lots of class features, like sorcerer's font of magic or warlock's pact slots, cut off at 5th level spells, suggesting that 6th level spells are supposed to be a major step up for 11th level PCs. But... as @Horwath points out, they kinda aren't. 5th level spells aren't crazy strong--excepting a handful, like wall of force and animate objects--and 6th level spells aren't crazy strong either. As a result, the 11th level power spike is not terribly coherent.
I wouldn't be opposed to the tier jump being at 9th level for 5th level spells, or 13th level for 7th level spells, but that would also take a lot of changes elsewhere to be an improvement.
I'm thinking I may create a spinoff thread about how 11th level PC tier could be improved.