I've had multiple times that by using apt-get autoremove, my entire Ubuntu installation has been fubared. It is almost nicer how Windows and Mac apps ship with all the required libraries and functionality they need, and you don't have to worry about it (both as a developer and a user). Add to that the confusion where programming languages have their own package managers (should I use Python's easy_install or the .debs?) and there's even more of a mess.
I've never had any difficulties on my Mac or on Windows due to a lack of a package manager, but I have had problems using apt.
I don't understand, what advantages does using a package manager have over simply shipping an app with the libraries/programs it needs? Yeah, you save hard drive space, but with hundreds of gigabytes of data, is that even important?