Frankly, I think they should.All of what you said may be true and Chicago schools may use more dollars per capita than other areas but overall Chicago as a whole uses fewer state tax dollars - considerably less when compared to the southern region of the state. The bottom line is the further you get from Chicago the less money is put into the pot and the more money is taken from the pot. Insert any other expense paid for with tax dollars and why can't the Chicagians ask the exact same question you did about Chicago schools about the rest of the state?
But they should also ask why they cannot capitalize on the economies of scale issue. Why they need to collect so many more taxes such as additional sales taxes, excise taxes, etc.
You do have extreme examples downstate like Cairo and East St Louis. Those will not be fixed by more cubic taxpayer dollars.
But that doesn't prevent Springfield from spending them.
Two-thirds of the population lives above I80. They can vote at any time to stop sending money downstate. There are 118 legislative districts in IL and at least 2/3rds of them are North of I80. So it's not like they don't have to votes to stop funding the spending downstate if they think Chicago is getting the short end of the stick.
The folks downstate are in the opposite position. If they think they are getting a raw deal, they don't have the political mass to change things in Springfield.
I'd say if Chicago has a bad deal, they have no one to blame but themselves here.