More info: https://fredblog.stlouisfed.org/2021/05/savings-are-now-more...
(Edit: Updated link to a more recent blog post)
This gave banks more wiggle room to sit out the pandemic without reducing lending at the exact wrong time.
So the Fed has done its job on the way down. Now they just have to do their job on the way up as well, or this money will eventually end up as new money in someone's pocket (via new loans) and potentially create inflation.
We had this unprecedented crash that clogged up global supply chains and caused a huge shift in what people are buying. We have massive government spending increases. I don't think it's possible to work out what impact QE is having on inflation right now or whether it will indeed be transitory as the Fed believes.
For that to happen you need enough credit demand in the economy.
It could happen, and, as you say, the Fed would increase the interest rate making reserves less available (credit more expensive), but the number of reserves in the system doesn't cause directly more money in the economy. It depends of the type of recovery.
They may justifiably want to keep interest rates low and loans easily available to help businesses and governments roll their pandemic induced debt until they can grow out of it.
But then some other credit worthy borrower comes along and snaps up those cheap loans to buy into some asset market that doesn't need any support.
And where they do have the tools to make that distinction they don't appear to be using them. I don't understand why they keep buying mortgage debt while house prices are already looking dangerously inflated.