Imagine the Flames without the City of Calgary. If they are foolish enough to go to somewhere like Seattle, they will NOT have it as good as they do here. I laugh at their thinly veiled, and empty, threats to move the franchise. They are more than a handful of clubs that would LOVE to switch places with us, dilapidated arena and all. In fact, it really pisses me off.
While I agree that there is an economic effect from having a sports team in the city. That effect does not, in a direct way, translate into an ability for the City to collect higher property taxes. Your argument makes more sense to the Federal, and to a lesser extent the Provincial government who receive most of the benefit of the increased tax revenue, and both are going to contribute zero to a new arena. If you want City money, then it has to be tied to some sort of revitalization or redevelopment initiative (to increase property taxes), and then you must comply with what is in the best interests of the City.
This is not about being stoic, it is about not being strong armed into a bad deal. Calgary is much more than the Flames, but the Flames are not much without Calgary.