The way out is a gradual reduction in the amount of. Interest allowed to be entered (e.g., 1-2% reduction per year) to avoid spooking markets.
And if business ARE allowed to deduct interest expenses, but individuals not, then rich people will just have their company own their house, and rent it from themselves (or some similar adaptation).
In particular, for real estate, if loans become more expensive, fewer people will want to build housing, making the market even more constrained. (Now, I do see reasons for making lending more expensive, but that would be for financial stability reasons, not housing.)
To "solve" housing, I think the main approach should be to encourage the supply side. Make it easier and cheaper to build, and harder for local communities to enforce their NIMBY inclinations.
Within reason, though, because if take to the other extreme, you may end up with an oversupply of housing in many areas, which can lead to slums forming.
Yes, there could be a hit to overall investment, and it could be argued to set a lower bound of allowing deductions for up to 50% of interest paid or something.
Yes, the benefit is less for married, because standard deduction becomes $26k so marginal deduction is an extra $22k, $9k/yr in the bank, $750/mth.