The character is still playable, just less effective. Characters can take up to three Consequences - mild, moderate, and severe. (These can be physical or mental.) Each of these is an aspect that opponents can potentially use against you. Mild consequences go away very quickly, moderate ones after a session, severe ones can take multiple sessions.
We managed to turn Marco's severe consequence into a moderate one with healing. So for the next session, an opponent could have used his "Bandaged Gut" against him, which potentially could be rather dangerous. (It would have given a bonus to hit and wound him, perhaps, or the pain might cause him to miss a crucial bit of repartee. Which in our games can be lethal in itself!)
Of course he plays! He'd be chatting up the guards, trying to manipulate them, for example. Maybe he'd even learn something interesting in the process.
Plus, knowing our GM, all sorts of interesting things would have happened while he was in jail. Maybe a local noble makes him an offer he can't refuse or the like.
None of it was automatic. I said Jurgen was "pretty good", not that he was amazing. He had to make a roll to get Marco's wound on the mend, and it was not an easy one.
Marco had the Fate point no doubt from a Compel, but I don't recall what from and it would take us rather far afield at this point.
What sounds easy? Obviously I did a fair amount of compression. There were a number of 'rounds' of combat, but I don't remember all the details any more.
Never fails? Did you miss that Marco got caught by the guard captain? That he got humiliated and badly wounded? He did achieve his objective of not getting jailed, but it cost him. And yes, we did succeed in preventing the war, but that's because our planning, deviousness, and skulduggery paid off.
Ludovico's attempt to poison Chloe failed miserably. Worse, she managed to administer a sedative to him!
GM: "You start to go woozy. You have time to say a sentence or two before you pass out."
Ludovico, in his most charming tones: "It's been a pleasure meeting you at last, cousin!"
Thankfully Jurgen managed to definitively wipe the floor with Chloe's other boy-toy and burst in before she could do anything nefarious to Ludovico.
That also was by no means guaranteed. Why are you assuming that because it was successful overall, therefore it was easy?