Why aren't natural disasters and terror attacks a good thing for the economy? No. Resources that are used to fix what gets destroyed would have been used in alternative ways. That's the basic premise behind the broken windows fallacy which is nicely described in this video (via Cafe Hayek).
The same criticism can be given regarding sports subsidies. The money used to subsidize sports, whether they be stadium construction subsidies, infrastructure subsidies, or operational subsidies, has to either come from taxes or borrowed. While the subsidies encourage economic activity, taxes discourage economic activity, offsetting any effect a subsidy would have. Borrowing to finance subsidies crowds out other investment activities, another offset.