Some examples of RPGs that have used only a single playable character to decent effect, for your reference, would be Final Fantasy XIII: Lightning Returns and, to an extent, Pokemon. The prior handled it by focusing on the 'dueling' elements; battles would largely consist of dodging/deflecting enemy attacks, opening them up to a counterattack, and then striking, with healing playing a very minor role unless you gamed the system. It also let you swap between customized 'classes' of sorts, similar to your idea of changing classes mid-battle, but ultimately this was more along the lines of switching stances to match the flow of battle. Pokemon, for its part, had other team members, but only let you fight with them one at a time. Individual battles were kept short and sweet, at heart being similar to a rock-paper-scissors match.
The common threads, as far as I'm reading it, are:
1.) Keep battles shorter and more direct, rather than being the drawn out hurt-heal-hurt-heal that you see in party-based RPGs. Consider limited or even *no* in-battle healing, to drive home the point.
2.) Focus on single enemies with unique gimmicks, rather than large parties of enemies. One-VS-many can limit your design options when balancing.
3.) Give the player access to different tactics that are specifically useful against certain foes. One character, but many options for what to actually *do* in a fight.
4.) Customization and personalization is key. A single character is much easier to become an 'avatar' for the player than a large group is - leverage that. It will help to avoid monotony from just the one character, and make things interesting before the fight even starts.
These are just ideas that I got from looking at a few examples of other games, and seeing how they handled it. Obviously, what matters most is what kind of game you want to make, and what makes the most sense for it. Take these ideas with a grain of salt, and try to find inspiration for your own twists.
