Oh, FFS! and move every time their rent goes up
No you've misunderstood. This isn't about moving house within the same area, it's about moving away from areas where all housing costs several times the national average, to normal areas.
I am assuming that most of the country is cheap enough that the cap isn't an issue, so it's the fraction of people who live in expensive areas that would be affected, and the members of that fraction would only have to move once.