If you had a dewalt charger go bad due to a generator, I would throw that trash away. These drills and batteries are built to be used in the field and recharged under less then ideal conditions. I’d be very doubtful that it died because you charged it on the wrong genset. This is coming from a guy who has a huge set up tools and works in the field under crappy conditions day in and day out.
Other folks were having the same problem, it had to do with the square wave the inverter was putting out. Switching power supplies have a similar issue, generally linear power supplies are extremely forgiving. Linear power supplies are the old boat anchor supplies that weigh alot due to the large transformers they use and coils in the filtering section.
Traditional generator puts out a sine wave, it may vary between 55 and 60 Hz if your engine doesn’t do a good job maintaining its RPM’s and also the voltage will fluctuate some. 99% of most stuff is fine with that as most switching power supplies are rated to handle 100-240VAC at a frequency of 50-60Hz.
Inverter generators either put out a pure sine wave or a square wave (might be also noted as a “Modified Sine Wave”)
Pure Sine Wave = no problems other than sometimes you may get RFI on harmonic frequencies.
Square Wave or Modified Sine Wave = you can have problems depending on the combination of inverter and power supply.
I was only putting my experiences out there for others to read, I have seen power supplies from at least a dozen manufacturers (all high end and respected) fail because of dirty/garbage power over the last 20 years.
Go ahead and enjoy whatever generator you want, My experience in Inverter Generators have been the EU series from Honda has been great.
But if all you are going to do is power some lights and strobes on your ice house a cheap generator is all you probably need. Hell I remember for years just lugging a deep cycle battery around and then throwing it on the charger at home.