Many tunes (both fiddle type tunes and songs) imply chords. But many do NOT do so at all. In many such cases, putting chords under the tune butchers it -- my opinion of course. English dance tunes often are very chordal in nature, Irish tunes often not, thus accompaniments are often not too much more than one chord, and players of things like bouzouki are often playing the tune with some drone strings sounding. To force standard chords on to these, in my opinion, does real harm, and one needs to provide supporting accompaniment (if at all) with considerably more skill and taste then "Where do I change from C to G?".

This is perhaps even more true for the songs. Listen (among countless others) to some of the old ballads on the Jean Ritchie ballad records from folkways (now reissued   on CD and available from Jean and George). TO put chords under these would be a complete nightmare. . .
sorry I cant entirely agree,standard chords fit some irish tunes,it really depends on the tune.
chords in open tunings work quite well for the guitar,for example first and fifth,with perhaps a sus 4 or ninth,very often the tunes in modes other than the major ,[the mixolydian and the dorian],work with chords providing the third is left out.
some tunes that are very major orientated sound alright with standard chords.
a chord is any combination of any notes more than two,two notes are dyads.
now obviously drone notes work fine as well
alot of scottish/shetland tunes wotk very well with the jazzy chordal accompaniment that Willie Johnson used.
yet alot of these tunes are in the same modes as the Irish tunes,so logically the willie johnson stryle should work for some irish tunes as well.
there is avery beautiful version of Barbara Allen performed by jean Ritchie.Ialso have recorded this sing with the concertina using chordal accompaniment[see youtube dickmilesmusic]very different form JeanRichie but it works.http://ie.youtube.com/watch?v=V_PoPY-mDpA