It did, but a capsule can do the job just fine too – for JWST, it is (or was) planned to do repairs using the Orion capsule and a mission module docked to it.
> And the orbiter's cargo bay certainly was useful to transport many parts of the ISS.
Kinda, yes. But an unmanned rocket could have done the same job, and likely cheaper than the Shuttle.
Most of the civilian Shuttle missions could have been easily served by other, much cheaper craft – but who knows what happened during the classified ones, it might actually have been cheaper to the taxpayer at large (if not NASA) to have one craft to serve both roles.
> The Department of Defense still actively uses a spaceplane-ish vehicle. It's just a much smaller unmanned one called the X-37b. Many folks speculate it's used to repair and refuel spy satellites, and potentially even rendezvous with and and hack enemy satellites. https://en.wikipedia.org/wiki/Boeing_X-37
We don't really know, but given how little fuel capacity it has and how long it stays in orbit, it's more likely that the DoD's stated purpose of long-endurance testing of new spy hardware is true.
1. Can it get to many satellites? Yes, it has good delta V, though I think you're mixing the X-37's delta V with its boosters and the delta V of the Shuttle orbiter without its SRBs and external tank.
2. Can it carry fuel for those satellites? No, not much. The X-37 has a maximum total takeoff weight of 5000 kg, while the Shuttle can get 27000 kg to LEO. Unfortunately, only one X-37 will fit in the payload bay of the Shuttle, so we can't actually lift five X-37s in the Shuttle.
Many large satellites weigh more than the X-37's total mass. The biggest individual consumer, the ISS, requires about 7000 kg of fuel annually to stay in orbit. A KC-135 in-air refueling tanker is much faster than an oceangoing supertanker, but you wouldn't use the former to empty an oil rig!
These satellites don't need altitude boosts-- they use propellant for orbital changes (e.g. to "re-task" a spy satellite to a new region). But instead of chemical rockets they often use xenon gas ion engines.
The key thing with ion drives is their "specific impulse." High-thrust chemical rockets are needed to get out of the atmosphere and perform fast burns, but ion engines are often >10x more efficient once already in orbit. And because there isn't a chemical reaction, there is less corrosion and they can last for years.
Refueling xenon for the ion drives of spy satellites would double or triple their mission lifespan. They don't need much -- maybe just a couple hundred kg. And this could literally save billions of dollars since these satellites are so expensive to build.
The Department of Defense still actively uses a spaceplane-ish vehicle. It's just a much smaller unmanned one called the X-37b. Many folks speculate it's used to repair and refuel spy satellites, and potentially even rendezvous with and and hack enemy satellites. https://en.wikipedia.org/wiki/Boeing_X-37
Generally I totally agree though-- capsule design makes way more sense for anything leaving or reentering atmosphere. The upcoming Orion are clearly in that directly.