Dear Mike,
I heard a story once: a new student at a music school asked a mate how he practiced. His reply was, "Without mistakes." Naturally, any sane person's reaction to this is: Hmmm. Pompous Prig Alert. But there is actually value in the advice. We all develop a form of kinesthetic memory about where our fingers need to be to make a tune happen. This matures over time. The thing is, we can equally develop a memory for mistakes ... and wind up playing the same section incorrectly every time. It's tough to correct that.
In my experience, learning a tune slowly and accurately before you work up to speed has its advantages. Yes, there is something to be said for how the tune falls into place when played to tempo, but I invariably hit those occasional measures where my fingers don't want to do the work properly. Then I have to go over and over that measure, and then I have to reincorporate it into the flow of the tune without hesitating (cause I know it's a flub-point for me).
When I tackle a new tune, I always tackle it slowly. And accurately. Over and over. The tempo comes naturally in time. But unlearning your mistakes takes much longer.
There is also this to say: music is about interpretation. You might find a traditionally fast song played slowly sounds incredibly luscious - and who's to say you can't play it that way? Not me!

'Course, I'll take a haunting aire anyday!
I like metronomes as a tool - even have one I use a fair bit. But at the end of the day, sometimes a tune wants to stretch a bit here and there, phrase a bit different to how you first heard it. Sometimes you want to hold a note longer, do a pick-up faster. You put your personal stamp on a tune and make it your own this way. And what could be more in keeping with that ancient Irish musical tradition?
FE