With the caveat that I’m not incredibly familiar with judicial dueling practices through history. Those got weird over time.
For those unfamiliar with the term, a judicial duel was a means of arbitrating a dispute. It’s a direct ancestor of modern legal systems. Over time there was a move away from deciding who was right via killing one of the parties or their representative. Feel free to insert a cheap lawyer joke here.
What little I know of the German Dueling Shields was that they were were intended to be used with a sword. The manuals I’ve seen do have techniques intended to be used if the sword is lost or, and otherwise unavailable. I don’t know if that was for certain kinds of disputes or if they were contingency techniques.
Shields that are specifically designed to harm the opponent are real. But, again, they’re designed to harm the opponent, but they’re not designed to be used alone.
I’m pretty sure, at some point in European history, a style like that existed. But, I’m equally certain it existed as a contingency, to keep a combatant alive long enough to replace their weapon if it was lost or destroyed in combat.
Fighting using only a shield is in the range of comic book nonsense and Dark Souls challenge builds. Not something you intentionally want to take into combat.
The shield exists to provide protection from weapon strikes. I mean, that’s the entire philosophy behind it. While you could just grab a shield and bash an unarmed opponent in the face, it’s not the entire reason to carry one.
If your character is just obligated to bash people in the face, then a truncheon or baton will allow them to do that, while being easier to carry, lighter, not obstructing their vision, and remain usable in tighter quarters.
This is just a “right tool for the right job” kind of situation. Just because you can use a shield to pound nails doesn’t mean you should.
If your character is facing armed opponents, then a shield alone isn’t going to be enough. Again, the idea is you have a tool to deal with your opponent’s weapon, but the shield itself isn’t particularly good at filling both roles. At that point they’ll need another weapon, whatever that may be.