Because buying property becomes less lucrative and requires more money with no mortgage interest tax deduction. I'm not sure anyone has modeled an accurate demand curve, but in theory this will impact housing prices.

But if you sell, you lose your grandfathered in deduction.. a supply cut that might cancel it demand cut

It's hard to imagine supply getting any lower than it already is, but yes that is potential offset.

And in California we still have Prop 13, which effectively locks long-term owners into their existing houses.