If these historians feel so strongly about this maybe they should pay the yearly £4.5m out of pocket?
That £4.5 million per year is a small price for social stability.
In addition the digital option has a likelihood of costing a lot more
What do you expect the liability to the state would be for all the wills getting wiped out, or modified, etc. Another way to think about it is, what would a private company charge the UK government to insure all liability costs of digitizing the wills? Especially since there are likely many individuals who are highly motivated to modify the wills database (many would benefit simply from destroying it).
I don't know the answer to that question, and even though I suspect it will be far greater than 4.5mm, the point is that's the correct way to look at this cost, set against all the liabilities and risks digitization opens you up to. And most never seem to consider the costs and risks of moving to a new system when pointing out the cost of the existing system as a reason to move.
They are also planning to keep some number of wills, if you kept say everything over a certain value you'd probably cover the cases you're imagining.
The UK budget is 1.045T of which this represents 0.00043%.
Abolish the police, which will result in far greater savings. Then if you feel strongly that your house shouldn't be broken into, maybe you should pay for costs for private security out of pocket?