But why would you use short-term fed paper to make money with your stake, when you could just plain buy short-term fed paper, without the risk of people "redeeming" it from you?

Backing a currency isn't about taking deposits from people. You can't back with deposits because your liabilities = assets then. You have to put your own stuff up, but then all you are doing is running the risk that people will redeem it away from you. Backing a currency is basically just giving your stuff away with extra steps.

Because you can get interest on the fed paper from money that isn't yours?

And if people redeem from you, just add a clause where if the liquidity pool is gone you have to wait X days before getting it redeemed.

It is yours. Again, you can't back with "deposits". If you have deposits, the depositors have a claim that encumbers the assets; you can't then "back" something with encumbered assets. You can only back a currency with unencumbered assets. And if you have unencumbered assets, why would you use them to back a currency?

Sure, I understand what you mean. It is still beneficial to the holder of deposits on which a small but nonzero yield is being received.