mounting a portable gen in a gen housing on TH - why not?

That sliding tray idea is a cool one.

The exhaust extension is a concern. That will put more back pressure and I can see that resulting in shorter life. I've used one of the Gen-turi RV units, it doesn't any back pressure since it's the warm exhaust that flows up the "chimney". Above all you want to make sure that you are not getting exhaust fumes inside the RV. Check the location of your C0 detector and consider mounting one in the bedroom closer to the generator area.

Good points - the air flow issues could be solved with electric fans I think. One of the main benefits in my mind is that it can run while being out of the rain / snow.

Because it's not designed to operate in a confined space. A built in generator has a fan that draws in a large volume of air for cooling and exits out the bottom of the compartment around the exhaust.

I would think it could be done as long you can divert exhaust away from TH and genny gets the airflow it needs to avoid overheating. Champion would no doubt frown on this type of installation and may not warranty unit (should they find out) used in this manner.

We have a Champion 3100 with remote start and it would have been nice to use our genny compartment at least to store it while going down the road, won't happen as there is an Onan installed. No biggie we just roll it out of the garage when unloading the toys.

I've heard of others mounting their portable generators in exterior compartments on a sliding tray, they then just slide their units out when they intend to operate them. Refueling the unit is an issue although adding an extended tank kit may alleviate the hassle.

There is no reason you couldn't at least see if it will work for you if you have the time and money. I would be happy if I could just store our Champion 3100 in the genny compartment while traveling down the road. Upon arrival simply pop it out and plug in shorepower cord.

As long as it got sufficient cooling it should work fine. I guess it would depend on how noisy it is as to whether it would be annoying from inside the trailer.