Ukraine

This would go one of two ways:

1. States would take the money, and money being fungible, State budgets for payroll would ultimately go down by that same X. Teacher pay might get a short term bump, but the long term result would just be States relying on the subsidy and using the extra budget room to do other stuff, without meaningful long term changes to teacher pay.
2. The money comes with regulations around teacher pay (to prevent the issue above) and many States refuse to take the money to avoid the regulations. The whole thing becomes a political football and nothing really changes.

Ultimately, the US is a Federal system which means a lot of stuff is handled at the State and Local level. A wholesale takeover of those responsibilities by the Federal Government is not as simple as "hand money to the States". Decentralized authority has long been both a feature and a bug in the US system, but it's not one which is likely to be changed anytime soon. The upshot of this decentralization is that States can use their authority to push and demonstrate policies before there is a national consensus on those policies. The downside is that some policies need to be fought on a State by State basis, which is a lot harder than a top-down, command style government.