The regions are much more marginal. Airports like MAN, STN, EDI, LTN, BHX have already paid their worth, so why shouldn't they pay tax? People at EDI and MAN might not be happy at NCL and LBA paying different tax bands, but while it may be a disadvantage (very small one) they already have a lot to offer AND already have a comprehensive network!
It's a great idea in principal, but then how do you address any disparity that comes from this.
For example, how would you prevent say, Ryanair moving a shed load of routes from Manchester to Leeds to make use of lower APD bands? That's not stimulating growth, it's moving it around.
How would you address a new route choosing NCL over EDI purely due to APD, it's not exactly fair? An airport should be able to attract a route in its own merit, not because of an artificial advantage.
Just because an airport is successful doesn't mean it should be put at a delibirate disadvantage just to appease the other.
For what it's worth, I also believe it's pointless charging LHR higher APD. The numbers of transferring passengers means many would be exempt from APD anyway!