It's not uncommon at all for ninjas to die on missions to be sure. Yumi was shown to have barely survived her mission with the butcher at the very first chapter. And now, the ninjas' situation is at quite bad, since they are heavily undermanned. So, a new prodigy like the MC joining their ranks could be exactly what they're looking for. As I said, ninjas are supposed to make do with what they have and try to resolve the problem. And yeah, the missions the MC has taken were all stuff that didn't go according to plan and turned out to be way more difficult than expected, this is for two major reasons:
1- Would you, as the player, really wanna see the MC doing a standard low ranked mission, where the they walk around with Karolina Schwartz for a few days, deliver her to her parents peacefully and head back to the village. Because that's exactly how the mission was supposed to go, but would be too boring imo.
2- Unlike today's time, where everything can be reasonably well coordinated, quests in medieval periods would've surely had more unpredictable turns. For example, the collapsed bridge in chapter 4 that resulted in the MC's party entering the town of the faceless god, would've just appeared on TV on the news today, and the party could've planned their journey better accordingly.