The demand for EELV-class launch vehicles (in the US) is almost exclusiely driven by National Reconnaissance Office, National Oceanic and Atmospheric Administration, and the Department of Defense, launching the NROL reconnaissance, GOES weather surveillance, and and GPS/Global SATCOM/DSCS navigation and communication satellites, respectively, all going to Medium Earth Orbit or Geostationary/Geosynchronous Earth Orbit, with a smattering of interplanetary spacecraft and commercial telecommunications satellites.
Back in the late 'Nineties it was assumed that there would be a market for low cost light/medium lift vehicles to support smaller telecommunications birds in LEO to MEO (e.g. Iridium), but neither the market for cheap satellite telecom nor the low cost reliable launchers really emerged, hence the retirement of the Boeing Delta II vehicle and the relatively few number of Lockheed Martin Athena and OSC Pegasus and Taurus launches. The failure of companies like Rotary Rocket, Kistler, and AMROC to develop genuinely commerical low cost launch services meant that the cost to orbit never dropped to a point that it was cheap enough to maintain large constellations of satellites necessary for operations from LEO. DoD launches for sub-EELV payloads have largely used the Minotaur family of Minuteman- and Peacekeeper-based launch vehicles.
That doesn’t mean that there is no demand for light and medium launch vehicles, however. There are plenty of vehicles available at a variety of lift classes from Russia, China, and Japan which are very competitive in terms of payload to orbit cost and which carry more commerical tonnage than the EELV vehicles. Many telecommunications and commerical surveillance satellites are launched on these systems, albeit with varying degrees of reliabilility. SpaceX offers the Falcon 9 and (soon) the Falcon Heavy, which are both EELV class heavy lift vehicles, but they carry substantially more mass than any single commerical payload requires, apparently driven not by commerical need but the founder’s desire for interplanetary exploration. The Orbital Antares rocket is a Delta II class launch vehicle which promises to fill the middle ground of light/medium lift vehicles, but the low rate of production and questions about future availability of the NK-33/-43 based engines make it questionable as a contender.
Much of the cost in launching stuff to orbit isn’t in building the rocket structures, flight software, and propulsion system itself, but in all of the processing, integration, and launch/range activities. In other words, the cost isn’t in the parts; it’s the labor. And since the labor is in roughly the same order of magnitude for a small vehicle with N stages as it is for a large vehicle with N stages, it makes more sense from a conventional standpoint for launch providers to focus on heavy lift capability. However, there are a number of ways that the processing/integration/range costs can be reduced by simplifying the vehicle design, accepting lower performance in exchange for greater robustness and reduced cost, and automating a lot of the acceptance and integration testing. This means redefining the processes which have been successful in the past but retaining all of the basic features that made them so successful, instead of just waving the “COTS” banner and blindly relying on the design to compensate for poor build quality, counterfeit components, and lack of qualification and characterization testing.
The Saturn V, as noted, wasn’t built to be a commerically viable vehicle and there is no conceivable demand which would require it for a profitable enterprise. It was a point solution to a problem of sending people to the Moon, and as a result it was neither cheap enough to be adapted for commercial use nor sufficiently expandable to provide the basis of a post-Apollo exploration vehicle. The Space Transporation System (“Shuttle”) on the other hand, was a broad solution to an array of capabilities that nobody was really asking for, and fundamentally was a transportation system to a space infrastructure that nobody built until the 2000s. Although it was expected to carry commerical payloads (and the government decision to shut down all other expendable space launch programs meant it was the only US launcher expected to be available) it was never cost-competitive with even the most expensive expendable launchers, and the often years-long schedule slips made it untenable even before the government decided to no longer accept commerical payloads. It mainly served as an object lesson to people who assumed reusability would translate into reduced costs (though whether a launcher that had to be largely rebuilt after every launch counts as “reusable” versus refurbishable is more than a semantic discussion).
There is plenty of demand for smaller orbital launchers; the question is getting them down to a cost point that makes them competitive with foreign launchers while still reliable enough to be useful and safe to launch from US ranges.