Lots of opinions here.
But I have actually done this.
Here are some facts.
My first TT a 75 Prowler. I welded an extension onto rear frame rails. It was beefy. It had to be, as the small quiet inverter generators did not exist then.
I wanted a quiet generator. The Honda ES3300 was my pick.... It was HEAVY at over 400#!!!
I semi permanently mounted it on the rear rack I had fabricated along with a cover to protect it from weather. It had electric start, so I rigged up a switch to be able to start it from inside the TT.
It worked great under tow, and camped. No issues at all...
Well there was one big one. The weight I probably added 600#s to the rear. So I had to be sure to load the front heavy.
With todays small Hondas, it would work even better.
As an aside, I have also ran the furnace while under tow. No issues there either.
Note: This was before the internet was invented, so information and misinformation (opinion) was not so easy to spread.