I think the theory is that it will prevent “hoarding” by forcing land owners to make efficient use of their property, or sell it, thereby lowering the overall price. It creates a less favorable risk profile for speculative real estate. You buy land to do something useful with it, not to wait for the next market boom before you sell.
I think the problem it aims to solve stems from the fact that once you own enough of the land you essentially can charge whatever you want.
More available because increasing the holding cost of underutilized land means owners would be marginally pressured to sell.
More affordable because the tax increases the holding cost of land which is factored into a buyer's purchase budget, much like how mortgage interest rates factor into a buyer's budget.
First let's assume the supply of land for sale is fixed. Of course land is in fixed quantity but I'm talking only about sales inventory – what is actively on the market to purchase. Say I can afford $4,000 per month. If property tax is $1,000 per month and interest rate is 6% maybe I say my purchase budget is $500,000. If interest rate decreases to 3% maybe I say my purchase budget is $700,000. Now consider if the property tax increased to $2,000 per month. Now if interest is 6% my purchase budget becomes $330,000 and if 3% then $475,000. In either case I still pay $4000 total per month. The economic incidence of the tax falls completely on the seller (the previous owner).
Now let's remove our prior assumption about the quantity of land for sale. we earlier established that land would be more available under a higher land value tax because of the increased holding cost incentivizing more sales. That increase in supply (of land for sale) should reduce the market price for land. I can either get the same land for less purchase price or more/higher quality land for the same.
The idea is that it penalizes speculators for just holding onto property without putting it to work. I am not an economist so I don't know which of the pressures would win out.
In theory by encouraging more efficient use of land, i.e. denser building. So you make land more affordable by using less of it per person for apartments.
Far fewer people are partnered, so that alone doesn't mean there is sufficient housing. Divorce/not marrying probably means we need 30% more bedrooms than previously required.
The average household size has not decreased significantly in the last 40 years (from 2.75 to 2.5), but units per capita has increased (currently around 0.425 units per person). We went from around 1.5% unit surplus to 6% unit surplus during that time.
You do bring up a good point, however. Nuclear families use housing much more efficiently than singles. For the good of the planet and others, perhaps people should consider the benefits of committed relationships.