Could Socialism Work in the Education System?

Hi there again,
Mutanatia here. There is a solution that I have been thinking about for the past few months about solving the solution to the poor funding of certain schools. The limitations placed on these schools are great: limited technology for teaching, limited access to teachers. The limitations in these degrees have placed an unfair burden on the children there.

The solution I have for this has not actually been looked into whether this would work or not, and that's where you, the reader, come in. It is in my opinion that socialism could work in the education system in one way: revenue sharing.

The way that this would work would be simple: A rich school does not need all of its budget. Does a school that collects millions in taxes for their budget really need to use all that much? I do not think so. It is often said that if you don't use the budget, you lose the amount of the budget you did not spend for the following fiscal year. I believe this problem would fix itself. All money not used for a budget would be put into a central "pot" for those schools who actually do need this money. Obviously, certain rules and limitations to how much money could be taken out of the "pot" would apply. Whereas 1% of the budget for a rich school wouldn't do anything, 1% of 1% of a rich school's budget would do a lot for a poorly-funded school. They could hire better teachers, or even update their technology, buy insulation for their rooms, and so on. I've heard of one such school that has to stop class every time a train goes by. This money could stop this problem.

Now, likewise, the reverse would apply: Normally, a rich school would not take any money from the "pot." But if a disastrous event, say, an earthquake were to happen and wipe the school out (heavens forbid), then the rich school, now needing to rebuild itself could take just as much money as the poor school did the day before.

How do we administer this? Right now, it seems like the best idea would be to make this be the ONLY function of the Dept. of Education. Arne Duncan frequently wails about how there are problems in the education system, but how he cannot do anything about it. This, to me, seems to be a practical concept that Duncan could use to better education and level the playing field, as he's so often sought to do.

Are there any systems that use this now? I look no further than the USA, namely the NFL. The NFL does the same sort of thing that I am talking about: the teams share revenue. This, in turn, prevents one team from having the BEST in the nation and making it one-sided (in theory, though not always in practice). Likewise, this revenue system that I speak would stop schools in poor districts from having the WORST teachers.

Thoughts?