Personally I don't find midi to be very useful for Irish traditional music- just too stiff in the timing department. I do find ABC format to be helpful in cataloging tunes. And midi playback is built into most ABC suites.
I use
ABCExplorer for ABC cataloging, archiving and display. It has an embedded midi player.
I do however work with midi material all the time for other music genres. Midi support seems to be embedded in most most players out there. So I don't think one bit about a dedicated midi player.
I use PGMusic's Band In A Box (BiaB) and their sibling products as assistants to writing and arranging including midi input.
I use Cakewalk's Sonar Producer for audio recording and production. I've used their products since they were midi-only production tools (late 1980's). I frequently start a recording by importing midi tracks from BiaB and build out and over those tracks to complete the recording.
Feadoggie