Restaurant Week is a legacy of a pre-Internet promotion designed to drive traffic during slower periods, get folks from the burbs into the city to drive extra spending, and showcase (back in 92 when it started) that NY had an increasingly energetic food scene. I believe a big proponent was Tim Zagat who obviously wanted to push his Zagat guides.

Whether it is still relevant today or not I have no idea, but I suppose nobody has come up with a better idea to replace it and there is still enough participation that it continues.

In the 90s I would debate that restaurants put out "lower quality" versions of regular fare. In fact, my recollection is that I was generally pleasantly surprised, as if the restaurants viewed is as an opportunity to perhaps introduce themselves to people who weren't in their regular customer target.