I shot a few 3 guns a decade ago and haven't been back now that I have the time, mostly because of the shotgun logistics.
I used a pump 20 GA 870 with an extended 7rd tube. No sights, no loading attachments, nothing. To be competitive, I'd have to have an autoloader, work on it until it was reliable(and IIRC most of them were not reliable before work and were picky with ammo after. Even my 870 pump had issues), get sights, find an ammunition brand that worked, get a mag tube extender. Then get a shell holders and/or those fancy vests with shells in rows clipped to the front. Not to be competitive with the magfeds or the fancy loading devices, just to have a better chance at shooting the stage under par time.
Shotgun shells are money I'd rather spend practicing rifle and pistol, as those are my important self defense guns. Adding a shotgun, shells, slugs, shell holders etc to my gear means I have to have a separate 3 gun belt instead of just using my regular rifle/pistol gear that's full already. I've shot many rimfire two guns with one large bag and one rifle case to carry everything. If I add a shotgun and paraphernalia to that, I might have to look at getting a tactical stroller gun cart to haul all the stuff between stages. I remember carts being almost necessary for 3 gun. Everyone had one.
Then there's the match format. TH3G got quite a bit more expensive and pro gamer focused, and the matches were always more shooting gallery and less defense oriented. To get a shotgun and start a 3G series again would mean putting a lot of money and time into a firearm and ammo I don't consider serious. I'd rather shoot 5.56 through my rifles at a more practical match.
If there were a "practical" 2 gun match with more emphasis on cheap self-defense/"combat" style shooting near RTP, I'd be very interested.
It's too bad Tim is 3 hrs away. And I'm still thinking of going.