What are the pros and cons of developing a web app without a known MVC framework vs. a custom MVC framework?

You may get a nice custom MVC and definitely there are developers who can buid an optimized better MVC then any other like CakePHP or CI, but the biggest advantage of having popular  MVC is that their support is like unlimited, and there are thousands of developers working to extend their plugins/classes. You get bigger support community which definitely a big help.

An interesting question but the only real issue is one of continuity. If your custom framework Dev leaves ( for whatever reason: hit by the proverbial bus, retires, moves away etc ), the question becomes how quickly can another dev pick up the pieces and keep you moving forward? In a world where the known frameworks are used, it's usually accompanied by a large community of devs passionate about the framework and stepping in is relatively straightforward. The large community also means that the framework is put through its paces and throughly tested to ensure minimal errors, especially around edge cases. They may need some time to learn the actual site / app code but it's a fairly simple process. When it comes of custom frameworks, if it's not really well documented, then it's much harder because the new dev will need to get inside the prior dev's head and understand the design decisions made. And that may take considerably longer with a greater possibility of more errors in the code in the short term.

I disagree. I've worked on both MVC framework and custom one. The only advantage of custom framework is that you can tune your architechture as you want. You can simply add extenstion and optimize them according to your required app. Still, I would recommend to use MVC frameworks, it save your time. Moreover these PHP frameworks are quite stable and are made by the developers who have faced web issues. These MVC frameworks have a lot of extenstions too. Moreover these frameworks are rapidly evolving with time.