In any case, the US system is already that the government records ownership (not for free, but for a small recording fee) and the title company charges for checking, and for insurance in case they get it wrong.
As just one example of how it can go wrong, here in Seattle it’s common to find out your lot is nine inches smaller than you thought because surveying technology is a lot better now than it was when your deed was written in 1908.
And we're not talking inches.
But, yeah, even inches (or any liens) can be an issue when it comes time to sell.
In 1800 land was sold in person only by people who knew each other, in front of other witnesses who knew everybody in town. It worked great, which is why some states (I assume like CT) never bothered with a registry. In the mid 1800s as land out west started opening up for settlement (skip the whole bad treatment of the natives) investors "out east" wanted to invest in land and ran into a problem: they didn't want to go out to the land, but they knew scams existed so they started hiring trusted people to travel instead and verify they property owner was really the person they were buying from. Some states have a registry and so you don't need that, the state tracks owners and verifies the people buying/selling really are who they say they are.
Prison is crime university and ID theft and related crimes are high yield low risk crimes.
The system doesn't care and such title thefts have been increasing for 15-20 years already
A number of US states historically had Torrens title, but most have repealed it, effectively converting Torrens titles to non-Torrens. Illinois had it – only in Cook County – until it was repealed in 1992. California abolished it in 1955. Virginia abolished it in 2019. Washington state abolished it in 2022-2023.
The big advantage of Torrens title is that it eliminates the need for title insurance, or at least makes it much cheaper. (You can still buy title insurance in Australia, but the Torrens title system significantly reduces the risk to the insurer, resulting in lower premiums–the risk it is covering is not that you don't have title to the property at all, rather risks such as the boundary fences being in the wrong places.) But in those US states which had it, title insurers wouldn't give you any discount for having it, and banks would still insist on title insurance to lend, nullifying the primary practical advantage of the Torrens system–the end result was your property was under a different title system which many didn't understand, which could make real estate transactions appear more complex, discourage buyers and lenders, etc. This resulted in political pressure from landowners on the system to be allowed to move off it, which is what resulted in it being repealed.
I think the US state in which Torrens would be most likely to be successful would be Iowa, since private title insurance is banned there. However, repeated attempts to introduce Torrens in Iowa failed, because the attorneys who investigate the validity of titles saw it as a threat to their livelihoods, and they successfully lobbied the state legislature against the idea.