There's a good precedent here for removing the charges. Until last year it cost £1-£2 for each company document that you wanted to download, but Companies House recently opened up the whole registry for free. They do just fine with the income that companies pay for registration, without needing the income from selling documents. I'm sure the Land Registry could do fine with the income from land registration (which are much higher than company registration fees) without needing to sell access to the documents.
Interestingly there was a line in the Tory manifesto about merging the relevant parts of Ordnance Survey, the Land Registry and so on to make a decent digital map of Britain that contains information about companies, land ownership, underground infrastructure etc.
I'm glad someone is finally doing it. The Tories have a pretty good track record on digital government (the gov.uk website is also great). Unfortunately that was the only clearly good thing I found in the manifesto.
It would be good if someone did that, but I'm finding it hard to imagine the Tories would be unusually motivated to make it happen - except possibly as another privatisable resource.
The current legislation is already supposed to make it impossible to own a company without being listed as a beneficial owner. It seems that in reality Companies House can sometimes be unexpectedly lax about forcing foreign-owned companies to comply with the law.
The current frontrunner for opacity is Scottish Limited Partnerships. Unfortunately fixing these is not within the capabilities of the Scottish Government.