I think the more important consideration is who is eligible to buy them.
Remove foreign owners.
Remove shell/holding companies. I'd remove corporate ownership of residential property entirely.
Remove 2nd/3rd/20th home owners.
Remove BTL/ other "investors".
Require that the people who buy them actually live in them, ie are not resident somewhere else in the UK for more than (eg) 2 months a year.
I don't think any of those are unreasonable for a country facing a housing crisis like ours.
Most of that seems reasonable. I'm sure they'd still be "expensive" given the location though.