@Solipsist
Apologies in advance for the text wall.
Sure I'm making some assumptions, but they're all based on statements in the story and/or established structures of how royalty/authority/combat works. Personally, I think it's a sign of a good story when there's enough details in there that you can start to understand the world around characters even if it doesn't explicitly tell you each and every detail.
I also feel the need to say this yet again, he already completed his main objective, the rescue of the elf, his only remaining objective is to get her safely out of the dungeon. Everything else is secondary. This is NOT a revenge plot, this is a rescue mission, that's it. Obviously our MC has a personal grudge with the prince, but that is not why he is there. (ch9 p21)
The guildmaster herself warns him twice before he even enters the dungeon, first, she warns him that the king won't be happy if anything happens to his son (e.g. If you do anything, don't leave loose ends), and second in reference to picking fights in the dungeon "Don't die a silly death" (e.g. Don't get yourself in over your head/know your limits).
He rushed to the dungeon with no preparations, no supplies, no real weapon aside from bow and a small number of arrows(?). He cannot survive very long in the dungeon, he has to be fast. We've already seen how deadly the dungeon can be in previous chapters even in fully prepared parties. We don't even know how he's going to get out of the dungeon again, the emergency portal disappeared after he entered, and he is on the 10th floor.
Izola detects activity (ch10, last page) and recommends they grab their evidence and disappear, this heavily implies two things, one they cannot afford to be seen, and two, they cannot be seen to be connected to anything that happened there (e.g. Loose ends). Any additional time taken to kill the prince, kill the knight (still alive), confirm the death of the mage (Magic/gods/hero's exist, gotta be sure), AND clean-up your obvious evidence (arrows), AND vacate without anyone realizing you're there is simply asking for way too much at this point. I mean, even recovering the arrows alone is going to difficult task, who knows where they all went. Heck, at this point we've already seen adventurers get mangled into a flesh lump and still recover, mind manipulation magic, possession magic, and more, does our MC even know at this point how to make sure someone either stays dead or if other forms of evidence could be gleaned from a corpse afterwards? He is a stranger in a fantastical world, and royalty have tendency to hold top grade goods.
The lives of the prince and his guards (knight/mage) ARE NOT IMPORTANT, literally irrelevant, if he can safely kill them he will, if he can't, he won't, their lives don't hold enough weight or value compared to the immediate risk (nearby activity/discovery). He is acting as an grab and go guy here, he is neither prepared nor equipped to handle any additional conflicts, it's an unscripted encounter like Izola warns him of that is the only concern. If he's discovered within close proximity to the prince, he will have to silence them (loose ends). The fight with the prince worked only due to well used ambush, surprise, and deceptive attacks. He now has very few arrows left (many now damaged/destroyed), a new conflict that he can't dictate the terms of while now also having someone to protect as well? Combat wise, he's running on fumes at this point.
Why do the prince and co not matter? Simple, his guards won't talk about this unless the prince does (loyalty/honor and all that), and the prince can't talk without bringing excessive shame on himself and risking retaliation from the elven kingdom, the Elf girl is also royalty remember. Also remember, they captured the person who handed the Elf over to the prince, MC also recovers the Elfs dungeon entry paperwork and shows them to the prince (which prompted a clear reaction), this is yet another form of leverage against the prince, since MC now holds a full set of evidence that implicates the prince in the crime. So once again, the prince cannot realistically ever talk about what happened there (Prince went through a lot of effort to hide what he was doing). The prince could hire an assassin or something himself later sure, but that's a different type of problem entirely (And is still risky for the prince if it fails, MC is holding incriminating evidence that others may also know). Note that if he did kill the prince, that would require him to also kill the guards, as they would most certainly talk since it's no longer about hiding shameful misdeeds, but the murder of royalty. Blackmail and threats are extremely common in every story of royalty under the sun for a good reason, it works very well. Also, it should be pointed out that in some ways, a prince under your thumb (or at least afraid of you) is a better outcome than a dead prince.
Now am I assuming some things here? Absolutely. Are any of them unrealistic though? No, I think everything I've said is fairly reasonable. Was this turn of events less satisfying than it could have been? Absolutely. Could I be proven entirely wrong in the next chapter? Absolutely! My excessive rambling is only really here to counter the unreasonable flood of comments instantly judging the story as trash because one thing happened at the end of a chapter that wasn't what they expected, I'm just providing other viewpoints. Do my words hold any weight? None at all! After all, I'm just a random internet denizen that reads way to many isekai stories. I'm just enjoying that this particular isekai story is so much more grounded than 99% of them, no cheat skills, no harems, a way to return to earth exists and it's within reach, MC is actually focused on that objective and isn't getting sidetracked, no hot spring episodes, limited power only gained through great struggle, actual real people shit like greedy manipulative merchants and discrimination that isn't convenient for the MC, earth weaponry isn't OP, other adventurers are as likely to beat you up as they are to befriend you, actually needing to learn about and understand the monsters in the dungeon to face them, an MC with an actual personality, etc.. etc...
