Jacob didn't want to entangle with Rosalia even if she offered herself to him because that woman had a peculiar attitude that can't be established by a humble background and only those who have lived their life in luxury and prosperity have this kind of attitude.
She was also quite a short temper and wasn't good at requesting, which made it clearer that she was used to getting whatever she wanted with a single order this make her background even more obvious.
Most importantly, the Star Mercenary Agency didn't have absolute records on who registered with them and how many times they can be registered with different names.
This was the biggest loophole in this system. As long as you can pay the price, you can take the test and get another identity.
