I'm not saying he can't be human, there can be emotional baggage with him, perfect example of this is Denzel in man on fire, he was a broke man at the brink but found his way back. I can even concede the MC becoming distracted around Emma because of what happened to the other Emma.
There are times when he could be professional as well, case in point the Charlotte incident, if all it takes is a woman in a dress to distract him, and i am pretty sure it was after what Lucy had told him about what had happened to her, then you aren't doing your job by becoming distracted so easily.
And for a guy who has his type of background should be able to pick up on certain things, like when a woman is not only staking out your house but when she also sits at a park bench not far away.
And again the moment Carter was going on about how Emma needs to go on her date. If warning bells aren't going off in your head that something doesn't seem right. And why Carter is all of sudden so interested in Emma's life, again you are not very good at your job, or maybe he was so distracted by Fox sitting there.
You can become attached to someone over time and still be professional, it's called work life and home life, over time i could see him letting his guard down but to let it pretty much happen straight away.
Again he doesn't have to be a super mega hero, guns blazing bodyguard, so i don't know why someone had to mention the incel comment.