If your policy change is going to harm the less fortunate then you should re-evaluate the policy.
A land value tax just shifts those who can't afford it out of their homes and hands more land over to the wealthy.
Land isn't the problem with housing. The problem is that developers have figured out it's more profitable to build fewer expensive properties than a large number of affordable ones. Not only do they have to do less work, but it keeps the market artificially low and so lets them charge more for what inventory they do have.
So they do just that.
And the residential development market has such a huge investment level to enter you won't see many willing to roll the dice on mass producing affordable housing.
Show me a home builder who has plans which are less than 3k sqft these days. You won't find one.
No one does that.