Generate the lion's share of income for
who? If a city's citizens are ponying up tax revenue to support a team, then the city should do it right, and be a shareholder in the team, and capture a proportional share of the lion's share of the income that flows to the team's owners. Forbes has a good breakdown of the profitability of the teams to their owners [1]. PBS Marketplace has a good overview of how much of that profitability makes it to the city [2]. You can read many papers examining the economic impact of letting a sports team walk, here is one [3] such paper.
Given the level of profitability to owners, the statistically insignificant economic impact of teams on cities, and the accumulated data to date continuing to support these conclusions drawn so far, city managers giving away valuable consideration as if they're supporting charity cases are simply using taxpayers to purchase extremely expensive political points.
[1] http://www.forbes.com/sites/mikeozanian/2015/09/14/the-most-...
[2] http://www.marketplace.org/2015/03/19/business/are-pro-sport...
[3] http://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1024&c...