There is no central bank neutrality?

There is central bank/tax collector neutrality, the Fed tax is liquid and easily hedged, or avoided.  So, that, makes banking neutral, but its mostly shadow banking that innovates as it is not the tax collector.

The cost of dealing with seigniorage is not large, but the effect magnified when a single sector, the regulated banks, are the tax collectors. Hence we want to make the seignorage a neutral inflation sales tax. Give Treasury the authority to issue inflation by fiat, under a contract we can agree on.

Whatever our philosophy peaches about this, one thing is certain. We cannot burden the banks with the function. We need fair banking, meaning banking that is not polluted with cross correlations. It can balance liquidity without checking that one sector or the other is in some crisis.