We won’t see the records themselves, but I’m sure we’ll get the tasty tidbits when Mueller releases his final report.
My mother kept her tax returns going back to 1975. Was pretty cool to see. I grabbed a few (her first, second, two 1980s ones, and a 1990s one) as well as a bunch of other old documents from the 1980s-1990s she had saved (IE copies of checks, banking statements from like 1993 etc). They would’ve been thrown out if she hadn’t.
I do believe this to quite insightful and correct. Thank you.
But that example can just as easily be used to make the opposite point. The Exchequer officials were nothing if not bureaucrats to their very core and so they had always kept multiple records of every transaction. That meant that while the tally sticks could be used if necessary to authenticate their other half, they had never been the primary record of those payments. The decision in the 1830s to burn the tally sticks was made in the full knowledge that there were other, more detailed and easier-to-use records of that information.
Why would it be wrong?
1960’s magnetic tapes degraded unless copied and re-written. But some may still be readable with some care: people continue to do that for irreplaceable data. 1960’s magnetic tape drives are still available.
1960’s paper tapes are still in good condition. Paper tape drives are less common, but also more robust and easier to fix.
That’s why I keep all my 1960s code on 96-column punch cards. 
When I learned FORTRAN in the 70’s, our tutor had his research project on the school mainframe. And he’d paid for a storage tape in the protected storage area. And since it represented 3 years of his life, he had the original punched cards in a box in his office on the other side of the campus. As the ultimate backup.
So it came as an existential shock to me when the university got rid of it’s last card reader, and notified users that they would no longer be able to read cards.