Centralized package management with a web of specific versioned dependencies is a huge hairball of state as it is. And when installed applications poke around inside your system, it only takes one or two oversights here and there to mess up this state.
Sandboxing, where feasible, minimizes shared state; usually at the cost of other things, but with modern software and modern resource constraints, our ability to deal with complexity is usually the tightest constraint. Sandboxing reduces the probability that things will break horribly (e.g. installing one app, and finding you need to install a new version of a library, which in turn means you need to reinstall 100+ more apps, which may bring in a new desktop or some other abomination).
And frankly, I think this is one of the things where you can't please everyone; personally, I rather have dependencies and know that a security fix in a library will fix all applications that use it than having to hope each developer releases an updated version, like on Windows.
But when they need integration with things beyond that? That's when it breaks down. That's when you need interfacing libraries that adapt one version of a library's interface to the next version, and very careful API and ABI design. I see that there's very little reason to take that approach for open source everywhere, but that kind of environment is essential for the stability commercial development needs.
Static libraries aren't the answer. A careful API and ABI interface to the core system, with managed compatibility from release to release, is needed. This is hard work; incredible amounts of effort went into making Windows 95 work as smoothly as it does, and some of the best war stories from Raymond Chen's blog date from this effort.
Things like preserving bugs in the moral equivalent of malloc to accommodate software that used memory after freeing it. This very concept - bug compatibility - is something that I see OSS community in general as being fairly hostile to, thinking that the software with the bug should be fixed, rather than making things work for the user. Of course the buggy software should be fixed; but making things work for the user is more important still.
