If I had to guess, the reason would be , that due to the nature of the transaction, and the multiple actors involved, that, from a legal standpoint, they prefer the immutability and distributed nature of a blockchain rather than a leaky old centralised system, which could potentially be gamed with more ease. Not to mention, that there would also be a greater potential for interoperability going forward.
Who's going to be paying to secure this blockchain?Exactly. It amazes me that there are so many people out there (and even here) who still don't get it.
Short answer, the same people that currently pay to run and access the UK land registry. Which is the government, and those that use the services pay for services.
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The problem with this, is that all the people you mentioned answer to (or are legally bound to comply with) a central authority, i.e., the government. So, if the government someday decides to reverse a transaction (Patriot Act-style, for example), they can instruct/force all the nodes to do so, which defies the main purpose of a blockchain, i.e. immutability. For a blockchain to offer true immutability and decentralization, the nodes must belong to independent entities that do not answer to a central authority, and hence cannot easily collude to achieve a specific goal, that may be against the common good.
Bitcoin is the first and only blockchain that has achieved true immutability and decentralization, as proven by its performance for the entire 13 years of its existence, where no entity, however powerful, has ever been able to reverse or invalidate a single transaction.
Using a blockchain while having a 51% attack advantage on said blockchain, is a contradiction in terms...