Fewer moving parts? I feel like a digital caliper can be made pretty crappy and take a lot of abuse and still work fine. Dropping them on concrete, the glass doesn't stick out as much? Although I have cracked the glass on a digital. It's easy to do, if you use calipers in conjunction with power tools or whatnot that vibrate, and you get lost in the project. When the earplugs are in and you're doing w/e, things vibrate off the edge of the bench all the time. When you're done not cutting your finger off, you look over, and sometimes it was your caliper.
Some of the low cost digital calipers eat batteries because of the plastic case that comes with them. The foam in the lid presses on the on/off button and can turn the caliper on when you close the lid.
It doesn't matter the on/off button, specifically. If it pressed any of the buttons, this would greatly increase the drain due to the current through the pullup resistor.
For me, the cases go in the trash. The tool is so much better when it's easy to access and is disposably cheap, anyway. For me, calipers are tools that are quite often used in conjunction with other tools; measuring things accurately is rarely the end goal. My garage shop calipers are stored in custom mounts right where they are used. Instead of carrying a pair of calipers back and forth, and having to retrieve them when they're "over there," I have one at both benches. My electronic bench calipers have no mount, but they also have first order accessibility. If I ever needed a proper case for say travel, I will buy another one for $10.00, and maybe keep the case. The existing calipers will stay where they are.