Lots of good stuff, but

They are allowed to inflate/deflate the monetary base

The Fed is not the cause of inflation/deflation, but you are correct that the Fed has tools to control the rate of change in inflation/deflation. When private banks lend, they create money which is the cause of most inflation:

https://en.wikipedia.org/wiki/Money_creation#Money_creation_by_commercial_banks

most money in circulation exists not as cash or coins created by the central bank, but as bank deposits. Commercial bank lending expands the amount of bank deposits.

Your other idea is interesting as well:

The best thing in my opinion is, however, that the money that the central bank is able to create for the federal government to cancel student debt can then be used to subsidize workers cooperatives

Should we cancel debt, or guarantee 100% employment so that students can pay the debt on their own?

Then the economy could transition to employee owned institutions. And students would continue to have some risk and skin in the game when choosing majors and what institution to attend.