I'd have to look into how the numbers work out, but most people seem to buy with a view to owning outright some time close - or ideally before - retirement. So when income drops, outgoings drop too, and they're left with a substantial pile of equity.
You might think that younger buyers would be interested in building up a transferable deposit with a combined buy/rent scheme, but it doesn't seem to work like that. I'm not sure why, because when property prices are exploding a part-share of equity is better than no share at all through renting, and potentially a reasonable investment.
My guess is the banks don't like the scheme because effectively they're forced into property price speculation. Normally it's the mortgage owner who takes all of the risk, and - obviously - even when equity is negative the owner is still responsible for the full amount of the loan.
So if banks co-owned property, a price crash would wipe maybe 10-20% off the nominal book value of the holdings.
But - when prices crash, mortgage defaults lose a similar amount from mortgage loans anyway. So the objection doesn't really make sense. And when prices are increasing, banks are missing out on a huge potential source of income.