The single biggest problem with a homebrew framework: Too few experts in the codebase.
Writing one's own framework is good fun (well, it is for the kind of coder that enjoys that kind of thing), but unless the ownership of the code is shared widely, it is a dangerous path to take.
I've worked in several places where they had written their own framework libraries. typically, the framework itself has been written almost entirely by one or two developers. The bosses are convinced that the framework code was a valuable asset, and the lead developers who know the code inside out are virtually irreplaceable.
The problem is that in every case I've seen, the code is full of bugs, security holes and poor practice. When the lead developer finally leaves, his successors are left to pick up the pieces. Sometimes they just battle on with the existing code; sometimes they undertake a large-scale re-engineering project; sometimes they switch to a third party framework.
The other problem that typically happens is that technology and user requirements move on. If you've written your own framework, you need to keep working on it constantly to keep it up-to-date. This is fine if the framework is your main project, but if it's just your back-end code, it will eat your time that would be better spent working on your actual project.
Finally, security. This is the big one, really. Many, many competent developers have written code that is insecure. In fact, if we're honest, we all have. Java wasn't written by incompetents, and yet Oracle had to issue a patch for fifty security holes this week. Every other piece of software you could name has had holes in it as well, and probably still has holes. By writing your own framework, you are categorically not going to be writing something more secure than any of the well known third-party frameworks. In fact its likely to be significantly worse, and you won't have the resources to go looking for security bugs. You'll have "security by obscurity" because no-one will have seen your code, but you only need to google that phrase to see what the security world thinks about that.
So in summary, I would say No; a home-brew framework is not a good idea.
Go ahead and write one anyway -- it is a great learning exercise -- but don't expect it to be as good as the frameworks already out there. If it was that easy, there wouldn't be any need for the existing libraries.