I still see no reason why a Star Wars RPG would be objectively better with a system that mechanically emphasized either emotional action or narrative tropes/storytelling.
I don't recall asserting that anything would be "objectively better". I said what I think would make a game fit within, or exemplify, Star Wars themes.
I'm a huge fan of Classic Traveller, as you (or anyone else) can see in my many actual play threads about that system. Classic Traveller is a sci-fi RPG. Classic Traveller is also a system in which distances between worlds, sometimes distances on world, the amount of money a character owns, the interest rate on their mortgage, etc, all count. To me, it seems obvious that none of that is relevant to Star Wars, and hence that Classic Traveller would not be a RPG that does a particularly good job of fitting with, or exemplifying, Star Wars themes.
But no doubt there's someone out there who's had a good time playing a Star Wars game using Traveller. Good luck to them!
So if I get what you’re saying, the mechanics of Luke shooting at a squad of stormtroopers should be different from those of Luke facing Darth Vader? How do would you implement that?
Traditional rpg would make Darth Vader a stronger enemy. Some would make Darth Vader a “boss” type villain, or a nemesis with additional abilities, closer to those of a PC, while stormtrooper would be a mob or brute squad à la 7th Sea.
So an emotional connection could leave different kind of wounds, but that requires another gauge than simple hp. And maybe they can even deal - wait for it - emotional damage! But joke aside, what did you have in mind?
Well, as I said I think there are different ways of doing this.
One is to have relationships rated like other abilities, with these then being able to be called on as augments. I'm thinking HeroWars/Quest as an example.
Another is to have emotional connection/conviction act as a buff - Prince Valiant and The Riddle of Steel are both examples of this, although with their own differences. Pendragon can also work like this, although its version gives the
player less control because of the way its Passion mechanics work.
There are also approaches that make emotional connection relevant in slightly more oblique ways, that exploit distinctive features of RPGing. In Burning Wheel (and Torchbearer, which is a reasonably close cousin of BW), players earn rewards (basically, buff tokens) by declaring and following through on actions that speak to the beliefs, goals etc that they have authored for their PCs. And the GM's job is to present situation that put pressure on those beliefs, goals etc (preferably in ways that increase tensions and create opportunities for trade-offs and pathos: eg I can save my friends, or I can get away safely with my loot, but probably not both!). In Burning Wheel, if nothing of that sort is at stake then the dice aren't rolled - the GM just says 'yes', and the action moves on until something of this sort is put at stake. The effect of this, in play, is to focus the action on matters of emotional salience to the characters and to encourage players to commit themselves (including via expenditure of their tokens) at moments of heightened stakes.
Apocalypse World, and similar games, uses the soft/hard move structure to put matters that the characters are emotionally connected to, and their choices in relation to those matters, at the centre of play - both in the way situations are presented, and in the way consequences are established.
Another device is simply to have simple vs extended conflict: BW, HW/Q, Prince Valiant (and plenty of other RPGs I'm sure) all have this, meaning that you can zoom out for stuff that isn't worth a lot of table time, while zooming in on the conflicts where the degree of investment is high and hence it is desirable to play through the detail. (4e D&D also has this in a somewhat crude fashion, in that a monster can be statted as a minion or more robustly, and a skill challenge can be set at a low or high degree of complexity - but a combat against a small number of minions in 4e will generally be unsatisfactory for other reasons, in the sense that the PCs don't really get to shine, and a good framework with zooming in/out won't have that problem in the same way.)