A feat of strength should be something that you either can or can't do.

Scenario: breaking down the door of the burning inn. Since it's a d20 ability check, the result is really swingy. Gale can succeed with 9 Strength while Lae'zel can often fail with 17. And this is the widest possible gap between a weak and strong character. Doesn't make a lot of sense. (haven't tried on patch 7 yet if they changed it)

Scenario 2: ripping Shadowheart's pod open is a DC 10 Strength check. Gale could do that with a negative strength modifier with 50% success rate. But for some reason it's a [Barbarian] option. Can't a Fighter with equal strength attempt it or is it only for Barbarians? Why?

Clearly a feat of brute strength shouldn't be about class, but Strength instead. There should be a Strength threshold before the Strength check is given to a character. Then the d20 roll could make sense as a stressful situation (burning building) or just random factors of having a bad grip or losing balance. I.e. Gale should have no business even attempting to force the doors open.

Shadowheart's pod should require 17 Strength to be able to roll a check, not being a Barbarian. Burning inn door, same thing. Then it makes sense why the flaming fist group can't force it open. Because none of them is that strong.

A weaker door could require 13 or 15 Strength to attempt to break. But someone with 9 Strength has no business getting a lucky roll and performing feats of great strength. It's not about luck.