I remember having this problem as well, it really drove me nuts. The playback API didn't seem to matter (Directsound, ASIO, WASAPI etc). I think I played with the buffer size/latency as well.
Can't remember if I ever completely fixed it, or how I mitigated it though (won't have MC reinstalled until I get my file server up and running) but it definitely involved playing around with the Start/Stop, Between Track settings and that kind of stuff.
I do remember that even AFTER a fadeout, I was getting pops/clicks like the OP is describing but I believe I managed to get that down to a minor level. My interpretation was always that is was some kind of residual noise/data in the buffer that wasn't being cleared properly (why else would it appear after a fadeout?). But this is clearly not an area of expertise for me.
Personally I am the kind of person who prefers hard start/stop and track switching (true gapless, not a crossfade) so I definitely found these issues annoying.. Glad I wasn't the only one experiencing them.
I don't think I've ever experienced it in other programs. But I could be wrong.
Anyway, that's my 2cents