> 1. People have mortgages with very low interest rates. If they sell the home, they give up that cheap mortgage for a much higher mortgage interest rate with the next home. So, they stay.
This may be true only in the US. In Canada, for example, the maximum term a mortgage rate is fixed for is 5 years, after which you have to "renew" your mortgage and renegotiate the rate. So a lot of people are already being forced into higher interest mortgages here.