I must admit that the separation of powers issue had not quite occurred to me, since the entire scheme is self-defeating and would scare holders of the US debt anyway. People would be (and are right now!) worrying a lot more about a credit rating downgrade or a default than a separation of powers concern.
Both parties have radical members. The whole reason the debt ceiling "crisis" keeps coming and going is because of a Congressional Republican faction, and the faction members are far more numerous than the number of Congressional Democrats seriously discussing use of the coin. The latter could probably be counted on one hand, if not one finger.
The coin always comes up because the topic gets amazing engagement for media outlets, and generally gets everybody excited for one reason or another--e.g. the sheer absurdity, or for the literati the technical minutiae. But it would never happen. More likely would be a default, but that's also not very probable as it only takes a handful of moderate Republicans (5 this go-round) to switch sides for a budget vote. That's why the markets don't care
This charade only happens so Republicans can show their base that they're serious about fiscal conservatism, and more specifically it's part of a very long-term strategy to undermine public support for Social Security. And any Democrats advocating for the coin are likewise doing so only to signal to their base (or readers) that they're serious about putting a stop to Republican obstructionism, which is a major topic and source of frustration within Democratic circles--impotence in the face of minority obstructionism.