> Term limits aren't necessarily a good thing
While your argumentation is sound, incubents for life are not great either - status quo tends to get more and more entrenched - bureaucracy keeps growing indefinitely even after system achieves base performance. All the problems of executive branch seeping into legislative.
When country starts to suck, people get disillusioned with politics, lethargic. This further amplifies the feedback loop - less informed voters, more need for term limits to enact at least some change.
Otherwise posts of career politicians are still replaced due to pawn exchanges, death and occasional corruption scandal - which luckily prevents efficacy converging towards zero as time goes. However members are keeping post for two decades or more in extreme cases, and we get very nasty things - paradoxically short sighted planning due to populism (because low quality voter base), rampant coat changing, high level corruption - old guard is well connected for it, compared to n00bs in office.
> if you replace people at too high a rate
It's an interesting game theoretic/social problem - design optimum algorithm to dynamically adjust term limits. Perhaps applying progressive handicap to ballot results depending on time already in office. But just like fixed term limits could be counterproductive, no term limits at all could be sticking head in the sand, hardly optimal.