Unless you're using it as an excuse to be video game-esque murder automaton, I don't see why being an orphan should really matter.

Sure, real life, it's not a small deal exactly, but from a fictional character position it only really matters if you're using it to justify the subsequent adventure. The "you're actually heir to an important such-and-such due to this hitherto unimaginable parentage you've suddenly discovered"-approach, "You killed my parents and I swear vengeance"-deal, "I was taken in by unconventional parental figure(s) and now I'm involved in the exciting things that their lives entail", or lastly and most common I think "I have to abandon my childhood and take steps into the adult world to survive, entailing a life of greater risk and expediting my life greatly as a result".

However, if you don't want to, simply invent a parental figure(s) and it becomes a non-issue. One of things I found kind of baffling about Spider-Man was his parents never mattered, his orphan status was just sort of this thing to describe his character without actually defining it any significant way. I suppose it justifies his aunt and uncle's advanced age relative to Peter for whatever reason that exists... but overall they fulfill the same role and significance in his life, and that's not really a problem. Peter has had an unconventional living arrangement, that's certainly part of his biography but it doesn't redefine him around it.

Saying "you're an orphan and thus lose any reason to have significant emotional ties to anyone" is - not implausible if you want to push your character into that direction - but it doesn't have to touch any real aspect of a character either and they can have all the healthy emotional bonds that you want. Likewise, having two living parents can be equally as calamitous for a person's narrative if you want them to, depending on who they are.