Maybe their management shouldn't be consolidated but their funding absolutely should be, into a single country-wide fund. The districts should then be paid an equal amount on a per-student basis.

You might say that this doesn't account for differences in the cost of living between different areas. I say that it's all the better that it doesn't, because if the funding is set such that it is sufficient to fund education in the most expensive areas (and it will be because these areas have the most political power), the relatively increased funding will allow the poorer areas to catch up.