So, that's obviously the approach Apple's taken, and it has numerous strengths. "Installing" & removing .app files is quite simple, but that's of course not the whole story. Both application support files as well as (IIRC) cache files linger around the OS until removed manually. This is typically NBD (well, no huge deal), but it deserves mention. Managing remnant traces of .app files requires either manually navigating the OS and deleting files, or using 3rd party apps. It's worth noting that these 3rd party apps basically do what package managers do, except only at the uninstall stage.
More importantly, when I use OSX, I most certainly am also variously using brew & make to install various pieces of software not packaged as .app binaries. While in a somewhat ideal world it's possible to envision a scenario where all necessary binaries for a given OS are neatly packaged in a preferred format, that seems unrealistic. If I'm still, in 2013, installing really standard tools with a Linux-style package manager on OSX, it's safe to say there's no way I could expect all my requisite applications to be available for a nascent OS with a fraction of its userbase like Haiku.
Lastly, even assuming all binaries that could possibly be executed on a given system are packaged as .app file (equivalents), I frankly wouldn't mind having a package manager available to install (copy), manage, organize & remove my binaries (including support files). A package manager is a ultimately a tool of convenience, it's simply more convenient when dealing with a more classical *nix path / dependency model.