Think you misunderstand.
They do increase *if* they can increase. So on character screen, there's attribute points and focus points - whereby attribute points are invested into the overall lines (e.g. Intelligence, social, endurance) and the focus points affect the learning rate for (under intelligence) Steward, Medicine, Engineering.
So if they have ZERO attribute points in an attribute, at the rate their XP gains in order to get an attribute point it (essentially) never happens. My game ended due to the blobbing of the Empire, and in the entire duration to that point not a single of my 6 associates gained an attribute point.
I am not aware we can preview the potential companions attributes before hiring them though, maybe this could have been avoided. However, even having (is it willlowsomething as medic?) she has no skill points to Steward despite starting with 40 or 60 Medicine. So trying to get her to level up steward (as she already had intelligence attribute points assigned, so just a case of needing focus points accumulating and investing) as well got her to about 18... and then no more no matter what happened. Why? Because there's no focus points to invest in stewardship in order to get her to learn past the imposed cap.
So the skill points increase the rate, but there's a cap limit on where you can go. No other companion had a single attribute point allocated to intelligence, so she seemed the best option to additionally level up. Just getting focus points for companion was equally impossible as attribute points.
Hopefully that clears it up? Basically, unless you find specific companions with specific attributes assigned and specific skill points assigned, you're screwed in being able to train one to perform as a role.
So why have roles and be assignable? The intent is good/fine, but the current balance is decidedly undermining it. I'm sure it's a bug as the grind otherwise is basically utterly insane to achieve it.