Your experience is interesting as I've lived in New England, NY and near DC for 15+ years and it seems like there are a lot of families with BYU ties in each place I've lived. It's not like the number who have ties in Utah wards, but in my experience it wasn't one or two families. And the majority of the active kids in these wards seem to want to attend BYU. It's especially true near DC where there are lots of BYU fans/alumni.

I agree with your overall premise that the church could do more to promote BYU as a church institution. It does get tricky though when dealing with people who didn't get into BYU although that's probably true everywhere.