When they eliminated the credit card interest deductions people didn’t stop buying stuff on credit.
History – when income tax came into play – the personal income exemption was above the average income… so only above average income folks and businesses paid income tax. The tax code reflected that it was geared towards businesses – since most people did not even have a mortgage. It wasn’t till the end of WWII that mortgages became common.
Prior to that people saved money, borrowed from family, but it was unusual to take a 30 year mortgage.
They’ve eliminated interest deductions for everything BUT homeownership, over time. I don’t think homeownership rates will change dramatically if they eliminate the deduction.