PPAs are a nice idea but a terrible design. They work well as long as they are kept up to date and they don't overwrite distro packages. But in practice as you've noticed they tend to be abandoned after a while, and they don't respect the rule to not supersede original packages. Together these two faults lead to terrible consequences, as time passes they corrupt your Debian/Ubuntu dependencies and lead to unsolvable situations. Basically your system reaches a dead-end where it cannot upgrade anymore (or only partially, which makes things even worse).

Aptitude has a very smart and determinate dependecy solver that can recover a system from this kind of situation but it usually involves uprooting most of it by removing and reinstalling a huge amount of packages, some of which are essential. It takes a long time, if anything goes wrong you're screwed, and you may end up with older packages than what you had installed, which may cause your user data for those apps to not be understood anymore, leading to malfunctions or crashes. So yeah it can be done but at that point you might as well do a clean reinstall.