Presiding Overseership hasn't been rotational since at least the 80's. It is the only local-congregation assignment for an elder that requires approval by the WTS; other positions (Thecratic Ministry School Overseer, Watchtower Conductor, etc.) can be filled by decision of the local body.
As mentioned, the PO is a first among equals, without any extra vote. However, just like in any organization, chairmanship does make for additional power and cotnrol. Chairing meetings, setting agendas, processing correspondence, etc. gives the PO the ability to bring up issues he wants to bring up, and bury issues he wants to bury.
The PO is also the clearinghouse for judicial information. That does not mean he is on every judicial committee; but he is the one in charge of informing the elders that there is a judicial matter, ensuring that a committee is appointed, etc. Again, by careful timing and selectve disclosure of information, the PO can affect the process.