Instead of just assuming that requiring ID leads to better representation, shouldn't we objectively analyze what choices lead to the best representation?

Requiring ID has the obvious tradeoff that it prevents some people who should be allowed to vote from voting. Furthermore, it can potentially lead to a system where people's votes are unfairly discounted because of administrative "errors" (e.g. interstate cross-check). From the evidence I've seen those problems are more significant than double voters or non-citizen voting.