Two categories where people don't want pricing to go down:
If you have plans to move and prices aren't falling everywhere, the proceeds of a sale aren't enough to buy elsewhere.
And if your bank owns the home rather than you, falling prices screw you over because you owe far more to the bank than you could make by selling.
So like what 99% of homes? If you rent you don't own it, if you own a condo you don't own it, if you own a house outright you are probably close to 1%.
Most of Barcelona is rent/condos. There is not a ton of 250m2 mansions in downtown Barcelona.
That's covered by the case of "property values go down everywhere"; you only have a problem if your property value goes down but the value of property you want to buy doesn't.
Right… you go and make that pitch. Run for mayor with it.