The GMCA is completely separate from the 10 MBCs, it owns zero of the airport.
Each MBC has had their budget cut by over 50% in the last ten years, and any income would just go to help bridge the shortfall in respective MTFS.
Burnham has very little power compared to the GLA Mayor, and certainly no power to take money out of each LAs budget. He couldn't even get Stockport to be part of Places for Everyone.
If your budget was £1b 10 years ago, but now £500m a £5m or £10m dividend for each MBC didn't touch the sides.