It really is very worthwhile playing a new tune over and over again at a much slower speed but with regular rhythm. Don't be in a hurry to speed it up to tempo - reinvent it as a slow air and revel in it that way for rather longer than you think is necessary. Then gradually increase the tempo to a little faster than you'll ever need. This works a treat!
I completely agree, and I want to express an additional reason for working this way: Different individuals or groups (e.g., individual "sessions") can have very different ideas of what "up to tempo" means.
... I recently sat in a session that played "Off to California" -- which I'm used to playing as a relatively slow, swaggering hornpipe -- at more than twice the speed I'm used to, a tempo I would reserve for reels.
... I think it's important that whoever starts a tune sets the tempo, which everyone else should follow, even if they are used to a different tempo. This should be as true whether the starter plays it slower than you're used to or faster. If you practice playing tunes at different tempos, you should have no trouble with that. (Starting slow and gradually working faster, as Samantha suggests, is an excellent way to gain this skill.)
... There are few things as irritating or -- in my opinion -- as rude, as people playing the same tune "together", but at different tempos, so that they really aren't together. Unfortunately, there do seem to be people who are so locked into a particular tempo for a particular tune that they aren't even aware they are out of synch with others. Learn to play a tune at different speeds, and you can avoid being one of them. Of course, you also need to learn to listen to and hear what's happening around you.
Furthermore, Samantha's recommendation of playing a dance tune as a slow air -- or otherwise at slower tempos than "up to" -- gives you a chance to experiment with and work on ornamentation and variations that you probably wouldn't have time to even imagine if you only practice "up to tempo", yet which you might be able to include with good effect at faster tempos once you've mastered them more slowly.