Are you talking about the cost of digitising? Or the cost of keeping paper records?
Because there's more to this than simply how expensive is the format that we keep them in. There's also how quick and easy it is to produce, to search, to share, to update. These are all positives when information is digitised that can't be done if your will is a piece of paper forgotton underneath your bed.
I'm sorry but this wildly over simplifying the issue to the point that the copper pipe analogy and hyperbolic language isn't useful. I respectfully hard disagree with this characterisation for the reasons I've explained in my other reply.
Putting a will (or anything other legal documents) on paper must have seemed totally natural hundreds of years ago but at some point we need to accept that we have different needs for these documents and different ways of capturing them.
I totally agree with you about security. That should be a principle in all of this. But that shouldn't constrain us to recording on paper. If security is paramount then design a system whereby you can verify the veracity and authenticity of the digital document and create secured controls around their handling - hint these systems already exist today. Tampering and theft is certainly an issue but realistically so is it if you still had paper. It's not uncommon for paper to burn, I have been told π.
Any system is fallible, but that shouldn't mean we remove it from consideration.