I have run a champion generator 4000W peak 3000W continuous for years.
It is not an inverter generator so it produces the "dirty power" and I have had no issues with it with three different trailers now.
I don't doubt that the electronics do not like the power but I have had no failures there.
If you properly manage your power consumption it runs the 15K AC without issue.
For light use I run a 2000W honda inverter
Now that said here is something to watch for with Champion or any other brand generator in use.
A friend had issues while dry camping with his champion 3000W generator
Everything went crazy in his trailer and the breakers started tripping etc.
The culprit was the regulator in the generator failed and produced max power over 240 volts which basically cooked everything electrical in the trailer.
Other than an EMS set up there is not many ways to protect the trailer I would assume.
Myself I have a little gadget I bought on amazon that simply plugs into an outlet and has a nice big digital readout of the power that I can keep an eye on
https://www.amazon.ca/gp/product/B00CDJRLKI/ref=oh_aui_detailpage_o03_s00?ie=UTF8&psc=1