Last year a dozen donuts at the local family run shop was $9, this year it is $12. My daughter's specialist doctor raised the cost of an office visit by 30% this year. The cost of a burrito at my favorite spot is up 25% in two years. I could go on. I care about inflation, and it is real.
Lower rates mean a lower payment, maybe affording the ability to outbid someone for a home you want. When rates go up buyers have higher payments.
The existing owner will have to pay taxes on the profits or reinvest in the same crazy market (perhaps losing a tax advantage).
I don't reckon any monetary distortions benefit the common people. Society benefits from money being a reflection of labor as much as possible. Everything else is extraction of value.
Mortgage payments are typically almost constant with respect to interest rates, because the monthly payment is what tends to climb to whatever value the market will bear. Instead, the home value itself goes up and down inversely with rates, such that the monthly payment remains approximately unaffected by a rate cut.