You wouldn't.
That's why I'm saying that if the NHL owned the AHL, you'd basically be doing away with (Not sure what they're called in hockey, in baseball, it's a PDL. The affiliate agreement), and reorganizing it in a way where that doesn't happen, and it's designed to regionally strengthen every team's brand.
For example, the Carolina Hurricanes would run the AHL Charlotte team. Because extending their brand to Charlotte helps them. Florida having their AHL team there isn't helping the Canes any. (I don't know think we can really quantify how much an AHL team factors in to NHL attendance, but it has to be at least slightly greater than zero. But opportunity cost is high of spreading your popularity in your state's biggest city
And Florida would get like Jacksonville instead, with Tampa taking Orlando. That kind of thing.
I don't think an AHL affiliate helps extend the major league club's brand much, if at all.
So look I'm a Winnipeg guy. When the Jets first came back they put their AHL affiliate (which they owned) in St John's NFLD. The team was quite popular - but I don't think it led to the slightest increase in Jets fans in Newfoundland. Similarly back in Jets 1.0 days, their affiliate was in Moncton - again no increase in New Brunswick Jets fans.
In a different sport - Edmonton (where I now live) used to be home to the AAA baseball club the Edmonton Trappers. They eventually left in 2004 (the cold weather we still get at season start was always a problem). During their time in AAA baseball they were affiliated with the Expos, Twins, Angels, Athletics, Marlins, Angels and White Sox. TO the modern day none of those teams are any more popular in Edmonton because we once were home to the minor league team.
And going back to the Jets - their affiliate (the Manitoba Moose) is now based right out of Winnipeg. The thing is I don't think the Jets have noticed any cannibalization of ticket sales. The price points are different. The fanbase is different.
Now look - when it comes to the Jets at one point the plan had been to try and put the AHL affiliate in Thunder Bay, ON. It's about 8-9 hours away from Winnipeg, but much, much further away from Toronto. So perhaps doing so would have helped extend the Jets "brand" into north-western Ontario, in a way that never happened in St John's. Maybe you need to be close, but not too close.
But the thing is - I don't think so. If you live in Thunder Bay you're going to continue to be a Leafs/Habs/whatever fan - even if you religiously go to Jets AHL games.