Skill matters for instruction. You must have a rating 4 in a skill to teach it. Also matters for multiple attacks, which you can only do skill/2 of.
Pool may be all that matters when rolling, but how you get there tells a story. An ex lone star officer may have 4 Agi and 4 pistols. He's not as fast as he used to be and his hands have a tiny tremor now, but he's been shooting for years. The punk kid he got saddles with thinks he is hotter than drek, but barely has a proper grip, let alone a good stance. He has 7 Agi and 1 pistols.
They both have a pool of 8, but gramps can teach the kid how to do it right, for gods sakes! Gramps can also make a multiple attack against two people, the kid can't.
If you have enough dice of various colors you might even roll different dice for attribute, skill, and gear. That way you can craft the narrative of the action around where the successes came from. Doesn't matter from a rules perspective, but is a cool way to differentiate characters with similar sized pools, but different ways of accomplishing them.