Certainly, third-party trading of such credit instruments would have to be prohibited. And in a broad sense, people could no longer freely contract with one another to accomplish any objective. I can imagine such a system. It is not impossible that such a system could exist. It would be a system of command and control of the purest type.
Nothing is gained by substituting one monopoly for another.
A lot can be lost. Such an input was once supplied irrationally through the monetization of newly mined gold and silver. So debt continues to compound exponentially, a process which cannot continue forever. At the very least, since it is empirically observable that debt continues to compound exponentially world-wide compared to real production and consumption, such injections are insufficient to accomplish the task. This means that the government is effectively paying interest perpetually on debt that it sells to itself, adding to, rather than subtracting from, debt.