You touched on my main point in all of this. I know this doesn't sound accurate in the world we currently live in, but supposedly politicians work for and represent the people who elected them. They are actually a politicians employer. I understand there are HIPPA laws that protect your medical records yet at the same time that doesn't absolve you from letting the people you work for at least know the current status of your ability to perform the duties they elected you to do.
As you eluded to, if anyone outside of elected officials did this they would have been fired. You simply can not just miss work for weeks with no explanation to your employer without losing your job.
I agree with you about term limits. Nobody should be able to control so much power for so long.
In addressing terms of age restrictions I also agree with you. But I mean as long as the Stones keep making new music they can certainly argue the point. I can see them saying, "But whatabout Keith Richards!?"

The biggest issue preventing these things from happening is the fact that to put these common sense measures in place would be dependent on the very people in power to have limits that would force them go give up that power. That presents quite the conundrum.