Yes. I think this is a useful model. Particularly the word "automatically".
Relatedly, excerpts from an article I read today:
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In less than two years France has gone through five prime ministers
...
The cost of servicing national debt this year is estimated to be €67 billion - it now consumes more money than all government departments except education and defence.
Forecasts suggest that by the end of the decade it will outstrip even them, reaching €100 billion a year.
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According to Françoise Fressoz of Le Monde newspaper, "We have all become totally addicted to public spending. It's been the method used by every government for half a century – of left and right – to put out the fires of discontent and buy social peace.
"Everyone can sense now that this system has run its course. We're at the end of the old welfare state. But no one wants to pay the price or face up to the reforms which need to be made."
https://www.bbc.com/news/articles/cvg9n6vr2eyo