I've got just over 25,000 miles on three different electronic shifting systems: Dura-Ace Di2, Ultegra Di2, and Sram eTap. Benefits?
1. I feel connected to the bike.
2. Not a single missed shift. Not even one.
3. Faster shifts.
4. I can shift while out of the saddle. I'm sure some do it on mechanical shifters, but I rarely attempted it.
5. The cool "zrifft" sound when I shift.
You do have to charge the battery occasionally. I get about 700 miles out of Sram eTap while riding every day. Di2, almost 1,000 miles. Doesn't seem troublesome to me. I'm charging other ride devices a couple of times or more each, per week.
Before I tried electronic shifting I felt the same as many who've posted here saying they don't need it. They don't. Like lots of other bike-related things we don't need. But I won't buy another bike without electronic shifting.