Morris dance tunes seem to be fairly evenly distributed between 6/8 and 4/4 (or 2/4 or 2/2) tunes: there are even a couple of tunes with variants in each time-sig. But with both jigs and reels there are only two main beats to the bar and the 1 and 3 of 1-2-3-hop coincide with the beats.Most morris dancers would probably not be aware whether they were dancing to a jig or a reel (but the musicians would know).
But then we don't have many banjos playing for morris - boxes, fiddles, whistles, even brass, but nothing picked or strummed.
WassaiL! V