Notice that Senate wasn't the only governing party in ancient Rome. Also "old" is relative. It meant "too old to serve in military", with Sulla's reforms the minimum age was 31 and even before that most influential senators were 40-50.
For emperors: out of 80 only 14 were over 65. 2 resigned/died at 66, 1 at 67, 2 ruled only few months, so really 9 out of 80. Rome is not the place to look for old rulers
Right you have to distinguish between the executive and legislative/judicial.
The executive being young and legislative/judicial being old was pretty typical across the ancient world.
Also people tended to not live as long in old age as they do now, we have lots of advanced medical interventions we can do to keep our old people alive and accumulating power and wealth.
Also Rome had a much healthier triangle-shaped demographic/population pyramid so they had more youngish people to draw on for elite qualities. They also had an active military culture so young people could actually prove themselves in leadership positions and make a name for themself. In the developed world in the current period that is not the case.
For emperors: out of 80 only 14 were over 65. 2 resigned/died at 66, 1 at 67, 2 ruled only few months, so really 9 out of 80. Rome is not the place to look for old rulers