If it was not clear, I am not stating that anyone who is in office is automatically the most competent. However, the entire point of a democracy is that you have the option to fire bad candidates. And yet, with term limits, when you do get a competent candidate in office, you do not have the option to keep them in office.
Being the chief executive in a system like brazil's results in a lot of power, for several perfectly good reasons, but it does mean you have to build in safe guards against that power growing.
Regular elections are good, but not sufficient, as a study of recent world history would demonstrate.
Term limits are not a solution either, as a study of recent world history would demonstrate. Clearly there is a need to check power, but perhaps the mechanisms that check power should not also ensure you will never have a truly excellent leader && increase instability from flipflopping policies && give more opportunities for people who will abuse power to take office and ignore the term limits because that's what people who abuse power do. A term limit is only effective against a mildly bad candidate who is not truly willing to abuse their power, because if they are willing to abuse their power they can just ignore it. In that way, you've created a system that caps upside but leaves downside uncapped in practice.
Democracies shouldn't have a "leader", they should have functional governments and strong oppositions. Focusing on a single person never ends well.
The fall of that system then came about when politically ambitious characters started developing more personal and long-term relations with their troops.
I'd say that's an argument for term limits: you want them to get good but not set roots permanently.
What it loses in efficiency, it gains in avoiding centralization, cult of personality, and encouraging standardization.
"Rome's tradition of having to serve in 'lower offices' before the higher ones meant that when aristocrats inevitably ended up in charge of entire armies they had some level of practical experience and learnings to draw on while commanding".
But yes, much is made of Rome's redundancy in terms of military strength and there's a lot of states during that period that had A King who did everything and then died in a battle and then everything collapsed.