Except PA suck, Alsa suck less than PA, and OSSv4 is hated by kernel devs and is hard as fuck to install. (yet on some of my machines audio only "just work" if I install OSSv4 :/)
Originally, the biggest was legal: When OSSv4 first came out (2002), it was not free software, so it could not be included in Linux. In 2007, it was released under the GPL, so that went away. However, this created animosity towards it from the kernel devs.
That explains OSSv4, but what about v3? OSSv3 was the only sound system in Linux 2.4 and earlier; why didn't they continue developing that? There are various criticisms of it; that it doesn't map well to modern audio devices. I am under the impression that a lot of the design criticisms of OSSv4 are actually against OSSv3, and they haven't bothered to learn OSSv4; but I have no real citation for this.
The OSS people don't really work with the Linux people, so the Linux devs don't want to invest a lot of time in someone else' code. This makes even more sense when we consider that Lennart Poettering claims there are only about 3.5 paid people working on sound in Linux--they would of course be fairly heavily invested in ALSA.
It is a long story, that I do not remember entirely and corretly, but it was mostly politics...
Part of it was because OSSv4 was briefly not open source, and this pissed off lots of people, when it became open again, there was some political fights (that I don't remember the reasons), and there is some technical details of OSSv4 that irritate the kernel people (like the fact that instead of being entirely on userland it rely on Kernel space to reduce latency, specially for games, and the kernel people say they believe it should be userland only).
IMO since OSSv4 was proprietary for a while, the kernel folks invested most of their efforts developing ALSA, so by the time OSSv4 opened up and became a viable choice, ALSA had much better sound card driver support.
Another big issue is that OSS doesn't support MIDI or USB sound card input, which is a pretty huge functionality gap for people who are using those features.
You know, you don't actually have to use pulseaudio on Linux. Both Alsa and OSSv4 work fine.