I understood why they are shooting it into a graveyard orbit, but not why they're actively turning it off rather than trying to get whatever science they can out of it. (I'm sure that if I have a basic idea like this, the people at ESA also had it, but I haven't seen the reasoning explained anywhere.)

I think this part of the Wikipedia article answers it:

> In order to maintain the fine pointing to focus on stars many light years away, the only moving parts are actuators to align the mirrors and the valves to fire the thrusters. It has no reaction wheels or gyroscopes.

So without "fuel" (reaction mass/gas) for the cold gas thrusters, it likely couldn't hold a stable attitude, and a tumbling spacecraft is likely quite useless because you can't even properly communicate with it, let alone use instruments.

I wonder what considerations went into not attempting to use it as a low-value probe sending out telemetry using a low bandwidth omnidirectional antenna (which I would expect the spacecraft to have for recovery in case something goes wrong). Maybe we already have all the science that would be interesting from other probes, maybe management/budget decisions, maybe it wouldn't work, but it would be interesting to see the decision making.