The Fed injects reserves into the system every time one of its member banks makes a loan. Those dollars also have to be repaid with dollars created by Congress deficit spending, so they are also temporary loans and obligations, not assets, to banks.
I think we are both on board with MMT so this is more of a friendly question/discussion. My understanding is that reserves are injected when the Fed buys treasury bonds, engages in repo activity, makes a loan to banks at the penalty rate, or pays interest on existing reserves. I don’t think member a member bank making a loan in itself results in a net increase in outstanding reserves. It is true that banks must obtain reserves to clear transactions, but they can do this by borrowing from other banks or directly from the Fed. Maybe I’m thinking about this wrong, though.