Thank you for posting this. I had also considered doing this, and the electrical information provided is useful. I have used a small HF generator for remote work.
I have dozens of battery-operated tools, many with dead or no longer supported batteries.
Milwaukee (12 Volt,20), Dewalt (12,18,20), Ryobi (18), Craftsman (12), Rockwell (12), Bosch (18), Porter Cable (12), all with different batteries. Now, they're doing 40 and 56 volts.
They aren't nearly as powerful or durable as corded models, and you always need a charged battery spare available if you want to continue to work.
Like most of us who have doing this a while, I also have all kinds of corded tools, some of which I would use remotely only occasionally, like a MIG or an air compressor.
Some of them from my father's electrical business are still going strong for over 60 years.
Cost, performance, durability -- battery tools don't come close.
However, they are lighter and easier to use for DIYers and those just getting started collecting tools. Whether you use them often or occasionally, you will need to replace batteries.
Obviously, it's nice to have both options.