Mafia stories aren’t my cup of tea to begin with; but if you really want to attempt to rewrite the common themes we see on Episode, then I think minimizing the mafia’s impact is not the way to go about it. For people working within organized crime, escaping is not as simple as “Okay, I found love; I’m outie.” It’s insidious, and it kills, and it bars you ever being able to obtain a normal life. I think it would be more realistic if you made it so that the LI tried to leave with all their might but couldn’t, if anything.
If you’re set on having the LI “escape,” at least be sure to show the negative mental health effects of pursuing (or in your case; being born into) that lifestyle and maybe even include some consequences for anyone that helped them get out.
I think one of the best things you can do for a mafia story is have heavy consequences, not just for villains but for innocent people too (ex: kill the LI or the MC; the cycle of violence isn’t over because you’re over it). If you simply want to write a romance story and you’re only using the mafia as a plot device to drive the MC and LI together, cut the mafia entirely.
To answer your question, yes, I think it’s romanticizing the mafia. But that’s always going to happen when you combine “romance” and “mafia.” 
I’m still trying to understand how the trend came about because truly there’s very little romance when gangs are involved. Lust and violent misogyny? Sure. Romance? 