So Brad Bird has explained this one quite succinctly;
He's quoted to say:
"What interests me is the idea of having a family, having there be a
reason to hide the powers," Bird said. "And once I had that insight
into what I wanted to do, I picked the powers based on who they were
in the family. And so men are always expected to be strong, so I had
Bob have super strength. Women, mothers are always pulled in a million
different directions, so I had her be elastic. Teenagers are insecure
and defensive, so I had Violet have force fields and invisibility.
Ten-year-olds are energy balls that can't be stopped. And babies are
unknown, maybe they have no powers, maybe they have all powers, we
"So, that's what Jack-Jack was, he was seemingly the first normal one
in the family and then at the end of Incredibles you find out that
he's the wild card, and that he's sort of the Swiss army knife of
powers. And that to me reminds me of the way babies can grasp
languages really easily and adopt them easily."
These traditional societal values for each family member have been transposed onto the members of the Incredibles family and, really, with this in mind, the most relevant "power" for Jack-Jack to have, as a baby in a family where the members are their powers, is all powers. Bird mentions how babies/children can adopt many languages, but babies moods can quickly change, they can get up to mischief, and they can be troublemakers exactly when you don't want them to. Jack-Jack embodies all of this, and who's to say his powers won't become more refined and singular as he ages, but as far as The Incredibles 1 & 2 goes, this is how his powers are expressed.
From the filmmakers conceptual viewpoint, this is how Jack-Jack's powers were decided, however as for a more actual and realistic reasoning, we can't know. The origin of 'Supers' never was explained as far as I remember the films, and so thus far we don't know if this is caused by genetic changes as per Marvel's X-Men, or simple magic, or an aeons-old curse, or some other reason.
Welcome to the community, by the way!