“Does the US Constitution inherently demand that our form of government be a Constitutional Republic?”
My sense is that the answer would be “no,” because any form of government may be altered or abolished if the people so choose.
The rub is...whether it is really the people or some other entity giving voice. We all know what happened in 2020.
Ah, but the constitution already provides a mechanism for legally changing the form of government. If that is not followed, we have consequences like 1861 or 2021.
“Does the US Constitution inherently demand that our form of government be a Constitutional Republic?”
As long as we are operating under the constitution it does.