Is it separation of power and ritualistic symbol?

We're used to figurehead monarchs now.

For most kingdoms, this was a recent invention. 200 years or less. For the nameless (you’ll note the family has no name) dynasty, this has been going on for at least a thousand years.

Between strong regent families and Shoguns, the Imperial dynasty has largely been powerless.

Besides residing at the center of all religious ritual.

Could this be why they've lasted so long?

No need to depose them for anyone to take power.