Is MVC really effective for a personal framework?
What MVC means anymore, due to its vague interpretation, is business logic, presentation, and input handling. So, unless you aim to design an application that does not involve any three of those, MVC is, in its vague sense, very suitable.
Often it can be more formal than you desire, however, as it demands physical separation of ideas into different code files. Quick and dirty tasks or rapid prototyping might be more quickly setup if the formalities are avoided.
In the long term, what MVC asks for is beneficial to the sustainability of the application in ways of maintenance and modification or addition. You will not want to miss this. Not all frameworks encourage the right practices, though. I am not surprised that you find the various implementations you've tried insufficient. My personal favourite is Agavi. To me and others, in a world of PHP frameworks that do not feel right, Agavi emerges to do the right things. Agavi is worth the shot.
Would it be a bad idea to use a module system?
MVC asks you to separate components of business logic, presentation, and input handling, but it does not suggest how to layout the files. I presume this is the challenge you are addressing with a module system. To answer your question: modules serve identically to sub-directories. If the items are few, its probably more hassle to bother with subdirectories even if the files could logically be separated into them. When the number of items grow large, its now cumbersome to locate them all and sub-directories become a better option.
Frameworks will tack on functionality that allows you to deal with modules as their own configurable entity. The same functionality could just as well exist without modules, perhaps in a more cumbersome manor. Nonetheless, do not consider modules primarily as a system. Systems are so wonderfully vague that you can adapt them to whatever setup you find suitable.
Did you ever write a framework for yourself? What are your experiences?
Yes I have wrote several frameworks with various approaches to solving the issues of web applications. Every such framework I wrote became nothing but a vital learning curve. In each framework I made I discovered more and more the issues with building software. After failing to create anything interesting, I still gained because when asked to make a program I could fully do so with justice.
I recommend you continue if this is the sort of learning experience you want. Otherwise, give Agavi a shot. If that too fails, ensure that you have a clear and detailed specification of what your framework will do. The easiest way to barge into making software, work really hard, and accomplish nothing is to not decide before-hand what exactly your software will do. Every time I ran into making code the only thing in my mind was I will do it right. What happened was a different story: oh, well I need to make a routing system as that seems logical; hmm, okay, now I need a good templating system; alright, now time for the database abstraction; but gee, what a lot of thinking; I should look to the same system from software XXY for inspiration. Therein is the common cry that pleads to use existing software first.
The reason I thought I could do it right was not because all the nuts and bolts of the framework felt wrong. In fact, I knew nothing about how right or wrong they were because I never worked with them. What I did work with was the enamel, and it felt wonky. The quickest way to derive your own framework is really to steal the nuts and bolts from another and design your own enamel. That is what you see when building an application and frankly is the only part that matters. Everything else is a waste of your time in boilerplate. For learning how to build software, however, its not a waste of time.
If you have any other questions, please ask. I am happy to answer with my own experience.