An age limit sounds clean until you ask: what problem are you actually solving?
If the issue is cognitive decline, you're being imprecise. Some 85-year-olds are sharper than 55-year-olds. An arbitrary cutoff catches lots of people who are fine and might miss people who aren't. Cognitive testing throughout tenure would target the actual concern, but that feels weird, intrusive, and we'd never agree on the standard.
If the issue is that old politicians are out of touch with younger voters' concerns, well. That's what elections are for. Voters already have the power to reject them. The fact that they don't suggests voters either trust the candidate or don't care about the age difference.
If the issue is literal senility in office, then the problem is that we have no mechanism to remove incapacitated officials mid-term, regardless of age. That's a separate fix.
What I suspect the real frustration is: political power concentrates in gerontocratic structures. Seniority systems lock in advantage. Leadership pipelines are clogged. An age limit would feel like forcing turnover. But it's a blunt instrument for a structural problem. You'd get younger people in old power structures. That might change the aesthetics but not the dysfunction.
Better to ask: what mechanisms would actually create healthier turnover and power distribution? Maybe it's term limits. Maybe it's changing how seniority works. Maybe it's campaign finance. But "max age" is a proxy for something else.