The idea that you can improve a tune by adding accompaniment is perfectly ridiculous.

As has been noted a few times already in this thread, it all depends on the ability of the musicians. I can, in fact, make a mediocre melody player sound better than s/he can make themselves sound. Melody players who lack advanced skills and experience often put forth a flurry of notes which, even if they are in the proper time, often don't communicate the rhythm adequately. The underlying throb isn't there. I can fix that.

With a good player or a bad player, I can accompany dance tunes in such a way that the accents and melodic lifts in the music that correspond to the footwork of the dancers are enhanced.

As has also been noted, it all depends on what you want, just the melody or the whole sound of the performance. Someone trying to rock out on Irish tunes without an accompanist is probably going to a lot like someone not trying to rock out on Irish tunes. If power and rhythm is what you're looking for, a good accompanist is a good thing. Or, for that matter, if what you want is a light classical feel, the accompanist can greatly enhance that. Or maybe you want a jazz feel, or a country/western feel . . .