Additionally, there are concerns about having the government itself involved with regulating inflation and business cycles. An independent Fed, at least in theory, allows for the fed to take a longer view of the economy even if politicians have incentives to care only about the next election cycle. All it would take is one conservative majority congress to semi-dismantle any MMT mechanism and completely mess up any "controls" put in place by MMT proponents.
That being said, it is refreshing to have different ideas being taken seriously enough to enough mainstream conversation. I don't think the field of economics is "solved" (probably far from it) so I think good ideas that challenge the status quo are generally good.