The key thing is that the rent you pay for locations will go to the commons, rather than private landowners, which makes sense, since locations are valuable because of all of society.
So some people will still be unable to afford to live in desirable locations, just as they can't afford to live there right now. The key difference is that even if they can't afford to live there, they will still share in some of the wealth created there, through the land value tax. Effectively, those who can afford to live in the desirable locations will pay some of their rent to those who can't (indirectly).
But then the demand of "giving everybody a shot at what they want" is not fulfilled. The people with not a lot of money don't have a shot.
"since locations are valuable because of all of society."
I saw that argument in the article, but I don't really think it holds up. I would say the people making a place high value already benefit from that place, they don't need extra taxes to benefit (for example if a place is great because of nice neighbors, those neighbors already live there and therefore already benefit from the place. If shops make a place great, those shops already benefit from the people shopping there. And so on). And sometimes people make a place worse, should the tax then punish them somehow?
"Effectively, those who can afford to live in the desirable locations will pay some of their rent to those who can't (indirectly)."
But then not because those "others" make the place so great, so in the end, what is the rationale? Also, isn't there a ground tax already? There is in my country?
I can agree that since property is a product of guns and more specifically police, and the government provides the police, some money can be asked for the service.
I like to talk about living by the sea, near a nice beach. That's a limited resource.
Of course you can build skyscapers by the beach, like in this photo: https://f.vividscreen.info/soft/9eba11ee5bc029cbef496435a40f...
It's just not the type of beach everybody wants.
So society is obliged to give everybody a shot at that 2 million dollar flat, no matter what their line of work or their qualifications are. How is that supposed to work?
Some things still are limited and will probably always be limited, unless everybody can live in virtual reality in their ideal world.