I've investigated further to come up with a more precise recipe:

- Start the machine afresh.

- Log in, play some music, everything is fine (only one pulseaudio
process, no crackles.)

- Log out and relog _as fast as possible_ (if possible, enter the
  credentials in SLiM in less than 2-3 seconds).

- 4 pulseaudio processes are up.  Sound is crackling when not playing
  anything.  It stops crackling when I play something.

- Log out again and relog (no need to be fast).  This time only one
  process is up but the sound is still crackling.  Killing the process
  fixes it.

- On subsequent logouts+logins, the issue does not seem to be
  reproducible.  I have to reboot.

Another clue:

After a fresh boot, the first time I log out I can see from a TTY that 3
pulseaudio processes are now running.
If I wait some seconds, they all eventually die and I can login without
sound issue.

Subsequent logouts won't spawn those 3 processes.

If however I follow the above receipe and log back in fast enough, an
additional process is spawned (which is normal) but the 3 processes remain.

Puzzling...

--
Pierre Neidhardt