"Otherwise it can just buy them itself to keep interest rates in check."
That would be no difference from "redeeming". Bond prices are determined by interest rates. When interest rate is the same as coupon rate the seller can sell for the face value of the bonds, equivalent to redeeming.
The difference is that the Fed pays the market rate, not the coupon rate, and by doing so at scale, the demand raises bond prices and reduces interest rates.
This is the opposite of what they've been doing recently -- selling bonds they already hold. Which is why bond prices are down and interest rates are up compared to a year ago.
