Running away would cause scandals which are problems. (Heir of i-forgot has eloped with xxx)
Running away from those problems would make those scandals worse.
As for MC's fighting prowess being made a big deal, he is a child soldier bred to be emotionless and kill. AKA a monster for the dumb people. Media being what it is, they love making things overblown even in reality.
"Jigokufkinlongname is going out with a child soldier. i-forgot is planning to employ child soldiers. Is i-forgot planning for a war? etc etc"
That being said, it doesn't change the fact that this is drama for forced plot progression (making MC a more emotional person, giving everyone a reason to learn his backstory)
I love this series despite the 'convenient drama' and the names I have been typing. I am really. REALLY. bad with names.