Leaving aside the design flaw of not being able to, as Alexander pointed out, alter the chosen session if you have a non-passworded account - I noticed that on a fresh Fedora 23 workstation install, merely running
dnf groupinstall "KDE Plasma Workspaces"
was not enough - once I'd done that, KDE was installed, but the gear icon in the GDM login screen was still greyed out. Rebooting (I wouldn't have thought it to be necessary, but figured I'd try just in case) makes no difference.
Following the steps in Christian's answer (installing kdm - obviously not installed as part of "KDE Plasma Workspaces" - then disabling gdm and enabling kdm) did the trick - the KDM login screen has a prominent 'Session type' button which pops up a menu.
Interestingly enough, not only does that menu show Plasma and gnome, it also shows gnome classic - something that obviously was already installed prior to groupinstalling kde (that and kdm are the only two things manually installed on this system so far) but wasn't selectable from the gdm login screen at all - so in the default fedora 23 workstation image gnome classic is installed, but inaccessible until you switch login screens.
I know the original question specifically referenced fedora 21, I'm just looking to keep this page relevant for people googleing the same problem in a newer version, as it does still exist (at least in 23).