The "high-heroic" era of Star Wars didn't really start until the prequel trilogy was released, when Jedi became omnipresent.
One of the biggest powerups has come from video games where you get to play a Jedi. It's not just that the prequel movies showed Jedi as more powerful than they were in the original trilogy, but also that video games tend to by their nature power up characters so that they wade through situations that would have seriously challenged or defeated the original movie characters. Then pretty soon you have video game characters force crushing whole Star Destroyers. It's the typical problem of power creep most intellectual properties have. Expectations keep getting bigger and bigger.
But you are absolutely right about the expectations of fairly low powered adventures in the early days of the extended universe, both in the video games and the fictional properties. And frankly, that was the game we at the time wanted to play. We weren't expecting to be Han or Luke. We were expecting to be inhabitants of the universe that they lived in.
IIRC, you could get about 10 points of advancement a session with a reasonably generous GM.
I think the book guidelines are more on the level of 3-5 character points per session, or at least that is what I've been handing out in my now two year old game with 40 or so 4 hour sessions. But, you are misunderstanding just how slow that is. One character point isn't a die. It will take usually 12 to 15 character points for a starting character to buy a die. After buying 10 or so die, the costs of new die typically go up to like 15 to 18 character points. I've handed out probably 120 character points as this point, but that's really only 10 dice or so. Starting characters have about 27 dice or so usually, so we're now up to about 37 dice characters after two years of real life play. In game though that represents just a bit over 5 months of adventures - maybe the equivalent of one season of Clone Wars or Rebels.
If we kept playing for like 20 years, the characters would probably start approaching main character levels of dice pools, but that would represent like years of game time with constant adventures. Which is supposedly what main characters in Star Wars have been through. By the time we get to the beginning of the Han Solo original trilogy he's already had years of adventures, then the trilogy puts him through 3 huge adventures of 8-12 sessions per book. He then has the adventure where he has to dump the spice that gets him upset with Jabba the Hutt, and only then do we meet him in "A New Hope". Then it's implied there have been multiple adventures between movies. In short, yes you could take a starting Star Wars character up to Main Character levels of power, but you might require decades of gaming to do that using the suggested advancement guidelines. I'm OK with that. It makes sense that veteran characters have game years or game decades of adventures behind them.
If you wanted to fast start that, you could start PC's with an extra pip or two in attributes and an extra 10 dice or 20 dice in skills provided you had reasonable caps on starting skill. But I see no reason to want to have a main character type PC without playing through their story so you know how they got there.