Its cheap light and easy to haul a half dozen humans home in a capsule, but its complicated and heavy to haul down immensely heavy satellites with a decent cross range such that you could land next orbit on friendly territory at all times.
Remember the shuttle "had to" be all things to all people, and the military demands ended up being VERY heavy and expensive.
At this time AFAIK nobody has the technical ability to snatch a Soviet spy sat and take it home, or haul strange and heavy (many ton) electronic warfare payloads over a target and land next orbit on NATO turf. Now, WHY you'd want to, or SHOULD you want to, are outside the bounds of this discussion, but the shuttle certainly had that kind of military stuff as a very expensive and very heavy design req.
Was the full crew necessarily just to put things in orbit? My impression was that most of the crew was doing other sorts of science and such because they might as well do so while the Shuttle's out in space (and later to get as many people into the ISS as possible per trip, which the Crew Falcon should now be able to do - maybe not to the same degree as the Shuttle, but certainly to a better degree than Soyuz).
At minimum, each mission had a commander and pilot. Then there were missions specialists and payload specialists, which depended on the specific mission the shuttle was carrying out.
There's always a lot of work to do, so it makes sense that they'd maximize for productivity.
It turns out not having to "shuttle" half a dozen humans up to orbit every time you want to get something up there is a good idea.