We're in the year 2122, so the teams would have to be fictional by now anyway.
If you like the ins and outs of HH (knowing how the player edits system works), you might be surprised how much you'd enjoy GMing against 29 other real people. We've got a financial structure that runs on the website, complete history of the league with a Hall of Fame and everything.
It took me forever to get my friend who also knew HH well, did lots of mods back in the day, to give it a try. It's addictive! He's been in for decades and decades now as well.
I've been in for over a literal decade. Good lord, I'm getting old.