The writers seem overly concerned about fans asking why doesn't Supergirl call Superman when faced with overwhelming odds. It is technically a fair question, but doesn't that also hold true of all the Arrowverse characters? Why didn't Barry Allen call in Supergirl to beat Savitar? Why didn't The Legends call in The Flash to help fight Reverse-Flash? Or any speedster for that matter?
Super-powered help would certainly have helped Arrow on more than one life-risking battle. Audiences understand though that the drama of any series is lost if the hero doesn't overcome great adversity. Viewers don't really expect weekly crossovers.
The writers know this and don't bother to justify these absences usually; it's just something that is understood. So why did Supergirl's writers try to explain that Superman doesn't help more because he isn't equipped to? In the second season finale, Superman blundered straight into a trap at left him thinking Supergirl was General Zod. Thus he engaged in full force against what he mistook for a lethal threat, and she knocked him out.
Later, he lets Kara accept the mortal combat against the Daxamite Queen because he says she is better than him. She very well could be, but this was the beginning of Clark starting to let himself off the hook when danger arises.