Except hockey teams make national advertisement dollars along with online betting and tv contracts. It absolutely adds outside dollars and funds many local jobs.
Once again, this doesn't create advertising space. The advertising space already exists. It could potentially increase the value of said advertising if the team becomes more popular, but that just forces advertisers to shift their focus from other targets.
Also, pretty much none of the TV money and Internet money end up back in local economies so it doesn't matter. The city sees no return on that.
The alleged selling point for a city is that it creates jobs and boosts the local economy by people spending money.
We know after decades of research that neither happens. Jobs move from one part of town to another, as does commerce.
Publicly funded arenas are basically always a vanity project and a poor economic investment.
The only way this sort of investment can be worth it is is it attracts large numbers of people to move to Tempe. That would mean you are actually creating new commerce and creating new jobs.
This project, and others like it, won't do that.
Montreal Expos prob from like...1997 onward
In that instance the league actively tried to kick them out of the league though.