The result of all this is code that is harder to maintain, even for those who know how to use said framework.
While I'm not against frameworks myself (in fact I argued in favor of them in this very conversation), I have become much more weary of them. In fact, after a brief affair with CoffeeScript I've even come to be more hesitant about using that or other 'transpilers', as I recently ran into the problem where I had to revert to plain js and I discovered that I'd lost some proficiency.
That said, it depends partly on the developers, and partly on the amount of structure the framework forces you into.
And that said, I suspect using a framework often serves more to alleviate managers' concern about maintainability than anything else.
There's one case where I would strongly suggest someone use a framework though, especially an opinionated one such as Rails. By following the Rails Tutorial by Michael Hartl, I learned a lot about best practices that I wouldn't have learned had I cobbled together a bunch of libraries. So for beginning developers, a framework might help them get started with their prototypes and whatnot.
Then again, maybe that worked for me because I can't help but want to look behind the curtain... I've certainly met my share of developers who never seen to wonder what's behind the magic.
The reason I don't believe you can write something cleanly with a framework and it be easier to maintain is that the framework is a black box of unknowns. So one option, as someone else has mentioned, is to try to fully understand that black box. But then you've just tied yourself to that framework. Wouldn't you be better served mastering the technology that the framework is written in?
1: jQuery proper. jQueryUI isn't too bad but is still a little more black box than I prefer. I really dislike jQuery Mobile for all the reasons I dislike frameworks.