Effect of lower interest rates on market prices (trick question)

[German E.]

Nobody knows how long mortgage interest rates will stay high, but one can start preparing by thinking what is likely to happen if/when they become lower, say in a year or two.  Most people seem to take it for granted that home prices will tend to go down, since demand will increase due to the cheaper mortgages.  But this is not obvious to me at all - notice that many people are stuck at their homes with a low mortgage rate that prevents them from moving.  When rates go lower, many will immediately offer up their homes for sale to move elsewhere, thus increasing supply as well as demand.  Thoughts?