What is First-Order Rewritable (and FO-Query)?
Part of the answer is in your question: if your language is FO-rewritable, query answering is in $\textrm{AC}_0$ in data complexity, which is almost as good as it gets. However, keep in mind that you have to pay the cost of computing $Q_\Sigma$, which might be expensive, though you have to do it only once.

Other good thing is that, for a FO-rewritable language, you reduce the problem of answering a query over a database with dependencies to answering a query over a database without dependencies. But again, the size of the new query ($Q_\Sigma$) might be exponential (or worse, but I'm not so sure) in the size of $Q$ and $\Sigma$ (because you have to encode the TGDs in $Q_\Sigma$ somehow). Anyways, roughly speaking it means you are reducing a problem to a simpler problem. I guess that's why it's very good.