I understand that he wants to get past the level cap and become stronger, but if he can reach a higher level by himself, his party may wonder why he needs them or more importantly, his party might request his help to defeat a stronger monster so that they themselves can reach a higher level cap. They're already doing whatever they want as it is so it'd be worrisome if they got even stronger. At least, if I were part of the authorities I'd be wary of adventurers who have somehow managed to get past the level 15 level cap if it's the standard. With that said, we don't know what kind of powerful humans are out there and level 15 seems far too low to be all there is to humans.
Also, I feel that the idea that he should get past the level cap in order to be feared is wrong because he can't have his status checked since it contains information that reveals he isn't a normal human. Although I understand that he seeks to become stronger and he really should continue on that path.
I wonder if he'll stay with that party. They're strong and they value his skills but they're also at the top of their little food chain with little will to improve their situation beyond what it currently is. So perhaps once he breaks this level cap he'll go on a journey once more? Honestly though, he's getting pretty comfortable himself besides the fact that he actually wants to grow stronger he still wants to call this city his home.