Except there are many episodes where Neelix acts like a jerk or an idiot for no good reason. Its why sfdebris usually has a stupid Neelix moment in almost all of his reviews of Voyager.
Neelix acted like a jealous psychopath and attacked Tom Paris for no reason in Parturition, almost destroyed Voyager with cheese in Learn Curve, got Ensign Hogan killed in Basics part II due to his massive incompetence and those are just some of the examples of him screwing up. He is a threat to himself and everyone on board the ship, his back story doesn't even begin to justify his incompetence and boorish attitude.
I think we can agree that Neelix did have some problems.
And I can also agree that his background story doesn't justify that behavior.
Still, I think that Janeway and the crew felt sorry for him and that's why he got away with lot of things he caused.
It was very important for Neelix to contribute and be useful. While Kes quickly settled into her new life on the ship and started to work with the Hydroponics Bay and as The Doctor's assistant, Neelix with his obssesion to be important for the ship and crew had to come up with own ideas about how to be useful, hence his role as cook, Morale Officer, journalist and all that. That was probably a reason why Janeway let him go along with all his whims. Not to mention that it was easier for Janeway to have him in the galley or pretending to be Morale Officer than to have him pestering her with constant visits in her ready room with suggestions for missions he could take part in.
"Fair Trade" is a good example of Neelix being so scared that he couldn't contribute anymore so he had to participate in illegal schemes to get things for the ship and contribute.
Here we also have clear examples why Kes and Neelix broke up. Their lives started to go separate ways as soon as they became members of the crew. Kes obviously had a crush on Neelix who she saw as her hero who saved her from the Kazon. But after a while, she started to see his dark sides, the jealousy, his over-protection of her and his constant interference in all her doings. Tieran may have finally ended the relationship but as we can see in the later half of season 2 and in season 3, the relationship had more and less ended with the two of them living separate lives.
As for Neelix's attitude to Naomi Wildman (or Greskrendtregk as I often call her), there are those who label Neelix as a pedophile. But I don't think so. I think he used Naomi as an excuse to come close to Samantha Wildman. Now wouldn't they had been a nice couple?