The point is that the council tax payers in Manchester have not voiced an opinion. It is the faceless bureaucrats and their political masters that have made the decision by the power they believe has been vested in them by Manchester's electorate.
I would venture to suggest that no elector in Greater Manchester cast his or her vote on the basis that their council was about to commit £1.5bn to buying an airport 200 miles from home.
The post facto rationale will be that the transaction will benefit the taxpayers through increased dividends, and therefore better services/lower council tax. As I have argued above, this is an optimistic view of the eventual outcome - and I hope that Manchester's taxpayers don't suffer a loss if their new acquisition doesn't work out in the way they hope it does.