Realistically, only the Spacelab, and ISS missions demanded a shuttle, the former because the lab was also reusable and needed to be flown home, and the latter, since the CanadaArm is useful for assembly of the station (which is why ISS has its own arm now). Maybe a few other things that involve the return of things from space. Aside from that, the shuttle itself eats into the payload capacity by far too much.
The entire truss structure would have been a real bitch to assemble without a "cargo truck" where you could just have the "crane" pick it off the "truck bed" and place it in position.
Realistically, looking over all 133 successful ISS missions:
4.5% (6) were initial commissioning/R&D flights, various flights without science platform or truncated flights
12.0% (16) were free-flyer return or satellite repair work/servicing
27.8% (37) were satellite deployments
7.5% (10) were Shuttle-Mir, including delivery of components
20.3% (27) were SpaceLab, SpaceHab, Astro, Atlas, SR
27.8% (37) was ISS assembly and supply/crew incl. MPLM
About 50% of the overall STS missions did demand a shuttle (half the Mir flights could have done without). Another 20% were missions that would have been complicated with another platform.
Before Challenger (i.e. in the first 18% of flights) half the missions were satellite deployment, 60% if you don't count the commissioning flights.