I entered the fray at a couple of MMT blogs.
There was some interesting discussion concerning consolidation of the Treasury and central bank, and how MMT portrays/misportrays the actual institutional details of modern central banking in order to make their message easier.
Between Depression and Hyperinflation at Winterspeak.
From the comments: technical details on MMT at Winterspeak.
The General and the Specific in MMT at heteconomist.com
Even with the BoE, the old way by which it could lend directly to government - via its "ways and means" advance/overdraft facility - has been effectively neutered. That facility was frozen in 1997 and has since been almost completely repaid. The upshot is that MMT can't look to the BoE as an example of its idealized "consolidation", and it can't give policy recommendations as if these institutional rigidities didn't exist.
The Treasury-Fed Accord: A New Narrative Account by Hetzel and Leach