Because it's a legal requirement to fly in a lot of airspace, to ensure that you show up on radar, and it's far easier to install one than to wrangle an exception. Of course it can be turned off, just like any other piece of equipment.
Even the B-2 bomber had a retractable radar reflector to defeat it's stealth. When flying in civilian airspace the reflector would extend so ATC could track the plane. Standard stuff to prevent collisions.
To start with, a reflector is passive, so it can't fail like a transponder. Failing is a problem when flying an intentionally very hard to see/detect airframe in dense civilian airways. Transponders only provide a secondary radar hit, while many (older) systems are looking for a primary hit to locate aircraft, which a reflector would do.
Any system that relies on a primary hit is going to have trouble. Something as simple as a composite glider is not going to show up well[1]. I'm not aware of any ATC system that relies on primary returns.
As for Googling it, that's an interesting picture. It's not retractable, but I suppose the point is made. Perhaps the B-2's is retractable. I did Google it this time and found nothing but some random airliners.net forum posts, not exactly reliable.
> far easier to install one than to wrangle an exception
You are talking about an agency that builds and operates planes that nobody else knows about. They can have any "exception" they want by just shrugging and saying the aircraft in question does not even exist.
All military aircraft have transponders because the air bases have ATC as well and (at least in the US) are near commercial airports they have to work with to avoid collisions during takeoff and landing.
Flying a military airplane through civilian airspace without participating in civilian ATC sounds like an excellent way to end one's career in the military.
Sure, they can just say the aircraft does not exist, if they stick to their own space. A U-2 is not going to do that.
