Here in NYC, I've almost never seen the church provide a luncheon--it's always on the family. And it's almost always at a restaurant. Because few NYers have homes that large (my ILs do; see 3rd graph).
For one thing, it's held after the graveside service, and the cemeteries are usually a ways away, so it's not like it's contiguous. People would have to come BACK to the church, or BACK to the restaurant, and most of them don't unless they're close family.
So the church doesn't hold the luncheons here that they have done for my family back in the Midwest.
Once there was a memorial mass for a sibling of my MIL or FIL who died in Europe, and afterward all the relatives simply showed up at my MIL's house and looked at her, waiting for food. My MIL hadn't been expecting it in the least; I thought it was SO rude. Nobody brought anything (true, since most of them didn't live close, they'd have had to stop at a grocery store, which they might not have easily located, but still!)