Yes, there are few tunes as boring as those that simply decorate some guitar chord progression, with no independent rhythmic or melodic logic.

BUT restricting yourself to slow airs, Irish or otherwise, is nuts. There are some ideas that simply can't be expressed in slow tunes. Matt McGinn's output is a terrific lesson in how to pick the right tune - he took melodies from everywhere (or pastiched highly identifiable types of melody) to fit an enormous variety of songs. Often the tune was chosen simply because it was as incongruous as possible.