Note that when you "buy" land this is quite limited. For instance anything that happens sufficiently below it (e.g. subway tunnels, mining) or above it (airplanes), you have no say in it.

Similarly a state could say, you license (not buy) land for construction/agriculture etc. use. This license does not include extracting oil, which requires a separate license. The land remains property of the state, but for specific uses (e.g. housing) you have a guarantee that you can keep the license for 100 years and/or can renew it under similar conditions. This is for example what China does: https://en.wikipedia.org/wiki/Chinese_property_law

Is that reducing the personhood of companies? (I consider that a good goal.) Saying that you must be a company to drill oil, and companies can only buy leasehold, not freehold.

Land is extremely limited in supply. If there is one thing that should not be openly bought and sold in markets (apart from humans) it is land.

How do you recommend allocating it, then?

Difficulty: without murdering millions of people to make it happen.

IIRC what some states do is that you can not buy or sell directly. Instead it goes seller -> state, state -> buyer. To a large extent the allocation is then still done by the market on the buyer's side, but the state has some leeway for overriding, e.g. highways, natural resources, environmental protection, affordable housing only, zoning.

Same as the society solved allocating humans. Instead of them being bought and sold on slave markets, nowadays we have companies leasing humans in exchange for a salary. You can do the same with land - lease it instead of giving asay infinite time ownership rights.

Which gov gets the money and why ?

Well, they seem to do OK in Hawaii. Not perfect by any stretch, but it isn't gulags and cold borcht.

The flaw in your argument is in definition of land ownership. You own the rights to use some portion of land somewhere. The rights are provided by other people, ie. a community represented by state.

'Buying' land, ie. transfer of rights from previous owner to new owner is a transaction which excludes the actual provider of the service of land rights, which is other people who will respect the new 'ownership'.

Current system is equivalent to giving infinite land leases, or very long like 100 years.

The way to fix this is to either have a yearly 'land tax' system to collect percentage of the land value or simply provide the land leases for like 7 years for commercial and/or longer for residential.

Each 7 years you'd have a land lease auction. Similarly to having a electromagnetic spectrum auctions or how DNS should be organized - periodic auction to prevent domain squatters to hold premium domain name 'real estate' near valuable domains (using levenshtein distance).

How did the person he bought the land from acquire it?

Well probably they bought it to, but yeah if you go far enough back there is probably some shenanigans going on with the land much as when you pass money around in America sooner or later somebody gets cocaine on it.