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I don’t mind if the city helps build the infrastructure support the stadium, or even donates land . . .

It was the latter issue that triggered the departure of the Brooklyn Dodgers and the New York Giants for the west coast:

Dodger owner Walter O'Malley wanted to build a new ballpark in Flatbush, over or adjacent to the Long Island Rail Road's terminal there. What stopped him: New York building and planning czar Robert Moses, who was hell bent on never allowing a privately-built sports facility in New York city or state again so long as he ran the planning/building show for both.

Moses obstructed O'Malley from acquiring the final parcels he needed to build the park. Moses also wanted to all but jam down O'Malley's throat a publicly-built stadium in Queens. (To which O'Malley said, famously, "If we play in Queens, we're not the Brooklyn Dodgers anymore.") Read very carefully: Walter O'Malley had no intention of leaving Brooklyn until he realised Moses's power was greater than his own and that he wouldn't get the final land he needed to build a new park.

The intriguing historical question: If O'Malley was that adamant about not moving to Queens, why didn't Moses offer the Queens facility to the Giants, who couldn't afford to build the new ballpark they needed but who didn't have the specific borough identification the Dodgers did?

Giants owner Horace Stoneham originally planned to move to Minneapolis (the Giants had a farm team there at the time), where a publicly-built park was going up as well for a major league team. Only when O'Malley's jig was up in Brooklyn and O'Malley reached out to him---O'Malley knew there would be no point in going west without another team to compete out there, considering the scheduling of the time and the then-furthest west team being the Cardinals---did Stoneham agree to move the Giants to San Francisco.

You can get the whole, real story in two books: The Dodgers Move West (Neil Sullivan) and The Last Good Season (Michael Shapiro).