Leaving generator wet or not

If it’s been working for 15 ,20 years, your method isn’t “wrong,” but most people prefer running the carb dry before long-term storage to avoid varnish or gum buildup. Letting it die on its own usually leaves a tiny bit of fuel, but with Stabil-treated gasoline, the risk is much lower. Either method can work; the key is just consistent maintenance and fresh fuel when you start it back up.

I use premium gas without additives in my Onan 5500. Wet all the time. Not a problem so far - 13 years. I do run it once in a while.

I run my generator once a month until it warms up. My fuel is always treated with Stabil year round, not to stabilize fuel but to clean (Double Dose). My unit runs itself dry at shutdown. 

Let me add another question to this - what if a generator has some varnishing going on, but not enough to stop it from running.  Is there a good additive to the tank that after running a tank will tend to clean up any varnish deposits without hurting anything else if it is left in the unit for awhile.

To summarize; it sounds both methods work fine.

One can leave it fully wet including the carb as long as they have stabilized fuel (I've always double treated 4oz per 5 gallons)

-or-

One can turn off the fuel and let the engine die so it runs dry

old fuel can still varnish even if it is wet,  in as little as 2 months.  you are useing a fuel stabalizer in it, I had to look it up to see what you ment,  so you should be fine over the winter and just start it up and burn it through in the spring.  a stabalizer usaly is good for up to 6 months.    I used to do that, then I switched to running the carb dry as my genny hardly gets used and even with stabalizer I was getting gunking as somtimes it wouldnt even run during a season.  now I am back to wet but I am using synthetic fuel for the last tank.  doesnt need a stabalizer, doesnt break down at all and it is always ready to go.  

As an FYI, my Honda 2200i has a control that valves the fuel and switches the ignition. Turn it part way toward off and the fuel stops, all the way it kills the ignition too. It also has a screw to drain the carburetor. I didn't realize it had these features initially, and after storage it ran poorly. Now fixed; I always run it until it dies, switch off the ignition, and further drain the few drops left in the carburetor.  I'm guessing the manufacturer thinks it must be important to get the fuel out before storage.

Your fuel treatment OCD is likely just enough to combat the effects of old gas.  Maybe combined with a pinch of luck. 
evaporation happens regardless. And some carbs evaporate out slower than others. 
for example I have an old Jeep that will seemingly keep fuel in the carb for a long long time and most every other carb from weed whipper to Edelbrock 750 evaporate out much quicker. 
So do what works imo as long as you’re aware of the effects you’re good. 

Fifteen to twenty years seems like a “proven result” to me; why change what seems to be working.

I start my generator at least once a month and let it run for about 15 min (generally I put at least some load on it 20% - 75%). In the winter I may start it twice a month or more depending on prevailing temperatures). I generally only keep a minimal amount of gas in it and freshen it often. Every 6 mo. or so I will drain it, put the old into a can with 6 gal of new, then pour a some back into the gen.

I have a second gen at the cottage. This one sits all winter without being started. So I run that one dry in the fall when we close up for the winter. Other than that, I do the same thing with that one.