I run on mains most of the time, and regard the battery as a lifed item. Its battery is down to half its original life after 4 years. So the battery is performing better than I expected it would. I bought a second battery with the original purchase on the assumption that, 3 years down the line, replacements would be hard to find.
A battery is good for around 500 full charge cycles. If you run on mains all the time, perhaps some people could argue that's not good for the battery's total number of charge cycles, but you're not using those cycles up at anything like the rate of running on battery alone.
Re deep discharging batteries, Li-Ion don't really suffer from memory effect, but they do age and need careful charging. The chips in most battery packs that provide monitoring and charge control also protect against any methods of "deep discharging" the cells.
So as I said, my approach is to use the machine in a manner most convenient to me, and to have a second battery in the house ready for the demise of the first one.