With an indefinite predicate, I think that the pronoun would be a mandatory addition to the subject if the subject were definite: Is ainmhithe iad na lucha. With both the predicate and the subject being indefinite, the pronoun is extraneous: Is ainmhithe lucha.
for what I've understood the pronoun is integral part of the copula: "Is <subject complement> mé/tù/sé/sì/muid/sibh/siad " is like a conjungation in Standard Irish: you can't replace the pronoun. So the logical subjec comes after the pronoun.
There's a complete explanation with several examples: https://www.duolingo.com/comment/4300985
For a comparison between English Copula and most of other copula structures: http://en.wikipedia.org/wiki/Copula_(linguistics)#Irish
That's with a definite article. This sentence doesn't have one, so it shouldn't need the iad.
Might this influence be the origin of the way of saying 'Them mice are animals' in some Am. English?