Coming at this as a long-time AGOT player, it doesn't really bother me that much, as I've just come to accept that level of abstraction in FFG's card games. In AGOT, the Character card category covers a whole lot: you've got standard people you might expect from the books/show, but other characters are massive armies or fleets, or even creatures like dragons and ravens (and one of those ravens is one of the most efficient and effective cards in the game).
Of course there's something slightly preposterous about the exchange "I shall attack with this army composed of thousands of knights" and "And I shall successfully defend, with this one dude," but is it that hard to suspend disbelief? For me at least, no, and I don't see myself having too hard a time accepting it when Artoo will stand in the way of Star Destroyer.
I don't know if anyone's come up with the terminology for it in this game yet, or if this is a concept common to many other card games, but the AGOT community frequently breaks things down into Ned, Shagga, and Jaime perspectives. Ned (you see the adverb Nedly a lot in our discussions, the other ones don't get adverbial forms often) is concerned with things being thematic; Shagga likes building up powerful combinations of cards; and Jaime is all about ruthless efficiency, whatever cards win you the game are the best cards, canon and thematics be damned. Not sure what could be used for Star Wars; Luke-as-Ned and Boba-as-Jaime maybe, not sure who'd be all about the combos.
I can certainly see the appeal in having things line up with the source material. There's certainly something satisfying about attaching Darth Vader's Lightsaber to Darth Vader, it's just obviously where it belongs. But I'm not going to hold onto that attachment, waiting for the "right" character, when I have a perfectly good guy in-play who would never in a million years wield a lightsaber in canon, but would wreak havoc with it in game. (That raven I mentioned earlier in AGOT? It can totally wield a sword, because why the heck not?)
Obviously that example doesn't really match up with the whole Jedis battling TIE fighters issues, but I do feel that it's somewhere in the ballpark by several degrees. I am interested to see just how important thematics are to so many people; I'm not really trying to discount your disapproval of how FFG has designed the game. If this is a deal breaker for you, it's a deal breaker. I just can't quite see myself from that perspective. The Star Wars license is just a bit more incidental to me; it's nice to have, and it got my attention, but I'm mainly here because I like FFG's card games and this one looks like it'll be a lot of fun.
The "Player Types" has a counterpart in Lord of the Rings; Boromir=Jaime, etc. so I wonder what FFG will do when they make the inevitable "Star Wars player types" article.
Going off your AGoT comparison, I will agree that while a lot of the mechanics are abstract, I do ultimately still get the theme of the IP through things like characters going after specific challenges, as well as the 4 player variant with all the titles.
True, there are some anomalies, like the examples you gave, but ultimately the card game has a Thrones-y feel to it.
Also, I have played all of the LCG's currently out (with the exception of Warhammer) and I've enjoyed all of them, but for different reasons, so it's a safe bet for me that Star Wars will be another winner. It's a bonus that it's the Star Wars IP.
When it all comes out, we'll see what kind of Star Wars flavour creeps through into the gameplay experience