@Cadence
From
mid-2018 to
mid-last year I GMed 15 sessions of Prince Valiant.
The three principal PCs are all knights. They lead a warband, a holy order that they founded - the Knights of St Sigobert. Their warband gets into fights, that being its raison d'etre. They also engage in jousts, have defended against sieges, etc.
Fighting isn't the only exciting thing that happens in the game, but it's a big part of it, as one would expect for a game of Arthurian-esque fantasy.
Here is a central rule on consequences for fighting, from p 26 of the rulebook: "Normally death is not an important part of Prince Valiant." It is up to the GM to narrate the consequences of losing Brawn and (if it happens) of being reduced to zero Brawn and hence losing a fight. The GM should do so having regard to the principle just stated.
This doesn't stop fighting, jousting, conflicts between warbands, etc from being exciting. Losing a joust can mean losing your gear to the victorious knight, losing the chance for prestige among your fellow knights, or perhaps just looking a fool. In our last session (the second one linked above) stakes included relieving a losing army (succeeded in part), retreating in good order (succeeded), defending against a siege (failed), pursuing enemies across the plain (one was caught, but the one carrying the kidnapped boy escaped to his own castle), then fleeing to another (friendly) castle (failed, so the PCs are confronted by their enemies just as they approach the walls of the friendly castle).
In your OP, I'm not sure which "many ttRPGs" you have in mind, but maybe D&D and other RPGs that have a similar mechanical and resolution framework? If you think it's interesting, I could say a few things about what features of Prince Valiant support the action I've described, compared to D&D. If you look at the actual play post you might also get a sense of it.