An EMP is really the least of your worries. (Or the greatest of your worries.)
That situation would be so, so bad that it would defeat a lot of prepping.
That said, in just about every other event, being able to produce a copy of your “paper world” would be beneficial.
For the cost of the scanner and the time spent, it can be a good recovery system in the event of even the least disruptive event such as storm, outage, or temporary evacuation.
While taking care of 9 elders at one time being able to access the important documents was a key factor to keeping stress down. I had better records than most of the physicians caring for them.
Yes...I also do digitize things, altho not to the extent you have (mine are not connected to my smart phone yet). Just on a jump drive.