Technically any class could be played as a single class. But the question is, would this build be viable at all, and if it eventually is - the extent of its viability and if it’s worth the sweat.
As having a char who barely finishes elite in pain, and can potentialy get 1-2 shot in ultimate, is hard to be considered viable and worth the trouble.
You say soldier and shaman, because of the HP nodes? Not enough.
The major issue with single classes is that you dramatically lack basic stats, and the poor HP/DA/OA increase is insufficient for the higher difficulties, also leveling is nightmare.
You got to be very picky with gear. To plan the gear you’d wear in advance, at any single point of the game, and rely on twinking - you can’t progress naturally, nor just slap and go. You will need specific gear with certain stats to enable the rest of the setup. The stat points have to be distributed even more carefully, and they are always insufficient, throughout the whole leveling proces.
When you hear someone to claim for single class support - the desire is exactly this, a mechanic/ability to somehow compensate for the lacking stats.
The game is not designed to be balanced around single classes, and every single patch brings content and equipment out of the reach of such builds. They could be mediocre at best, or serve as a personal challenge.
Basically, playing a single class is gimping yourself on purpose, and is just painfull with nothing worthy in return.