1: everyone who's got a borderline repayable mortgage to get anything in the overheated market and hasn't increased earnings by some 20-30% since then goes bust. This creates a wave of increased supply.
2: everyone's willing to buy gets way less loan amount for same repayments. This severely reduces demand at current prices.
3: 1+2 force prices down, meaning some people end up owning banks more than their house is worth. In the US the banks are in trouble, as people start walking away from their mortgages. In the EU such people are stuck with negative equity.
Such a scenario is outright disastrous, so no sane government will try it. So, the only way out of low rates is to increase this gradually enough to not create visible waves. Which means all 3 happen, but at a magnitude where most people do not notice.