This toy model ignores defaults and fiscal spending.
Defaults destroy debt in the absence of growth (in the process transferring wealth from creditors to debtors). Fiscal spending crates money with no debt (in the process transferring wealth from savers to borrowers). These counter-currents let the system stay stable while credit flows from savers (via equity) and creditors (via debt) to investments and borrowers.
Leveraged systems have a multitude of steady states in a zero-sum environment. Even more when tastes and preferences change as human tastes and preferences do.
> growth in fossil fuel use are very closely tied
I have debunked this in another comment [1]. Energy intensity of GDP has been falling for decades. The carbon intensity of our economy is falling faster.