So, the idea I believe is that they partner with various established players within the industry , in conveyancing, legal, HMRC, banks etc... and these guys who participate will/can run nodes to support the chain, and so the cost will be shared by them (and they will reduce their margins, and increase their profit by doing so)
The idea, that , it will be cheaper to maintain, than the current system(s) , more easily accessible, much much faster/streamlined, and far less prone to being gamed/defrauded.
So why would the land registry not just run a private secure database and charge fees to cover development costs? All the problems and expenses you decry are issues with the bureaucratic structure, not the underlying tech. A bureaucratic structure that isn't likely to take well to immutable databases, at that.