Good point about price heterogeneity. My family mostly buys recession stuff anyway, so our consumption bundle isn't likely to see major price declines even if "the price level" comes down.

As an aside, I don't believe MV = PY, because I don't think most of the variables are conceptually well defined. However, one of my favorite sayings is "All models are wrong, but some models are useful." and I do think that can be a useful model.