What distribution are you using? I just booted up both the Xubuntu 19.04 live cd and Ubuntu 19.04 live cd, and it's letting me remove Pulseaudio, no questions asked. It is also not required on Arch Linux, and Gentoo as the anon confirmed.
If you want to try it, open the terminal and if you are a Debian/Ubuntu based distro, sudo apt-get autoremove pulseaudio
and then reboot when it's done. I did notice that it would remove ubuntu-desktop and ubuntu-desktop-minimal if you are on the base Ubuntu distro, but you could still do it on Xubuntu no problem.
Xubuntu:
apt-get autoremove pulseaudio
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following packages will be REMOVED:
libpulsedsp libspeexdsp1 pulseaudio pulseaudio-module-bluetooth
pulseaudio-utils rtkit
0 upgraded, 0 newly installed, 6 to remove and 0 not upgraded.
After this operation, 5412 kB disk space will be freed.
My point is: https://packages.ubuntu.com/di... This doesn't require Pulseaudio in the 4 distros I've looked at