But there are more satellites up there than just US ones
It seems, to be fair, that the military was probably just as disappointed in the shuttle as civil space enthusiasts were. Unlike the civil space programme, however, the US Air Force is carrying on with the spaceplane idea.
The "concepts of operations" which the Rapid Capabilities Office hopes for out of the X-37B seem likely to focus on the same things the Air Force originally wanted from the Shuttle: mainly the ability to recover horrifyingly expensive surveillance hardware from space for repairs, replenishment of manoeuvring fuel and/or upgrading.
Possession of a larger X-37B, for instance, would have avoided the international furore which resulted two years ago when the US government decided to shoot a crippled spy sat out of orbit with a missile-defence interceptor rather than allow it to fall into the atmosphere uncontrolled.
Retrieval capability alone might justify the Air Force continuing with X-37B and possible larger successors, depending what the secret running costs of the "black" space programme actually are. However the design of the robot spaceplane, coupled with the talk of improved heat shielding, suggests that sneaky, low profile cross-range re-entries may also be a card the US military yet aspires to have up its sleeve.
If you want to get out into the wilder speculative realms you could postulate a mission lifting off to retrieve, not a US satellite, but someone else's. The initial launch would be explained as delivery of a normal secret payload, but in fact the spaceplane would lift empty, scoop up its target on one pass and return to land on a "Mission 3B" style profile without ever flying above a hostile telescope or radar station. The owners of the sat-napped spacecraft, out of sight on the other side of the world, would never know what had happened to their kit.
Less aggressively, missions of this sort might instead make a close pass by opposition spacecraft without anyone knowing about it - maybe just to get a good visual or electronic look at them, or perhaps to interfere with them in some suitably deniable way. This sort of thing would perhaps be practical with the existing X-37B; there'd be no need for a larger follow-on craft.
The US itself is known to be quite paranoid about this sort of thing being done to its own satellites: it is spending a lot of money on kit which would let a satellite's operators know what was happening to it in such an event (normally it would simply go mysteriously offline) and on dedicated guardian sats intended to watch over other US spacecraft even when they're above other people's airspace.
In general one can be sure that if the US military is worried about being done to, it is also thinking of ways to do unto others as well. So perhaps the Iranians are right - maybe the X-37B is in fact intended as a space fighter or interceptor of sorts.
There's a US Air Force factsheet on the robot spaceplane here. Readers may also be interested to note that a second X-37B has already been ordered by the USAF. ®
*The White Knight is best known for carrying the Ansari X-Prize winning suborbital rocketplane SpaceShipOne up to ignition height. It has also carried out a lot of other, less visible work for various US government customers.