Not receiving tax revenue from a multibillion dollar development does have costs/consequences. Ideologically, I'm generally opposed to the money that flows from cities/municipalities to large corporate entities and I do think there is a good argument that the Coyotes were trying to hide behind the 'private financing' terminology to ignore the benefit of these tax breaks.
However, the point being made by
@Xerloris is that the tax breaks would have been from taxes on the revenue/profits derived from the development. If there is no development and the land continues to just be an environmental concern, the city is still receiving zero tax revenue from the land to put toward schools, roads, police, or anything else. Considering that the land is currently a very negative value asset for the city, I'm not sure that development is going to happen without the city offering financial incentive to a developer. Building on former mining and waste disposal areas without any existing infrastructure is generally a huge pain in the ass. I think this is a situation where there is a good argument that this land is going to generate zero tax revenue for the city over (at least a lot of) the period of time that the team would have been receiving the tax breaks.
The 'cost' of $500M in tax breaks isn't just $500M of losses to the city when the alternative is a peace of land that generates no tax revenue.