It actually might be *easier* to have separate play/pause and stop buttons. You're right about the one-button approach not working well for players like Exaile that support pausing streams -- both the pause and stop operations should be available. That's unrelated to this bug, however, so I'll open up a separate bug for that. (This one's actually caused by a bug in Exaile, which I still need to report to its developers.)
It actually might be *easier* to have separate play/pause and stop buttons. You're right about the one-button approach not working well for players like Exaile that support pausing streams -- both the pause and stop operations should be available. That's unrelated to this bug, however, so I'll open up a separate bug for that. (This one's actually caused by a bug in Exaile, which I still need to report to its developers.)