Finder of things, Doer of stuff
I honestly think that the Pilgrim powers are one of the worst, if not the worst, mistakes made by the film. We can talk here about how Pilgrim powers are really very limited, and how they make sense, and how they have nothing at all in common with Jedi powers in Star Wars... but to a casual audience, you've got a sci-fi film set in space, and there are people with special powers, and it all sounds too close to Star Wars. And while I couldn't point to anything in particular (it has been close to two decades), I do vaguely recall various reviewers pointing out this connection. Pilgrim powers contributed nothing to the film (every single instance of Pilgrim powers being used in the film could be made to work without Pilgrim powers, to no detriment for the plot), but they unnecessarily evoked an uncomfortable similarity to Star Wars, just at the time when The Phantom Menace was coming out.
I should add, by having the Pilgrim powers conveyed through genetics, the movie made the exact same mistake as The Phantom Menace did: it destroyed the "everyman" feel of its main character. Originally, Star Wars was about a farm boy who masters these special powers that (potentially) anyone else could master, and goes on to save the universe - a fantasy plot where anyone could identify with being Luke. Originally, Wing Commander was about a character-less player character who barely even speaks a word, so that the player is able to pour their own personality and background into him. In Wing Commander the game, Blair wasn't special because he was a Pilgrim, Blair was special because the player is amazing. Then, 1999 comes along, and we get The Phantom Menace coming along and telling us that actually, Luke was special because he had a high midichlorian count, and no, you really shouldn't be identifying with him. And the Wing Commander movie, which tells us that actually, Blair was marked as special from the start, because he's got these special Pilgrim powers. I think that hits at an almost subconscious level, where it's really impossible to have a rational discussion about how actually, Blair's navigational powers didn't have to make him a great fighter pilot, so if he's a great fighter pilot it's still because the player is amazing. And you could see this in the discussions of the time, there was a lot of anger about Blair's special powers, and no amount of explaining that actually, Blair can just do maths very quickly, helped. The player was being depreciated.
Ultimately, the movie should have gone in the opposite direction as far as it possibly could. Blair should have been as "normal" as humanly possible. An everyman, who's being constantly told that his life expectancy on the frontline is three weeks or something, and being constantly told that he's not up to the task - and then proving himself in an amazing way. This would have worked just fine for a character arc in an air combat film, it's been done before - and it would have felt so much better for the fans in the audience.
A Wing Commander film without Pilgrims would have probably been a better choice. The pilgrim plot (in it's original intention, not the end result we got) on it's own is an interesting story and Blair's abilities are tied to that plot so I disagree to some extent that the movie Chris Roberts set out to make (based on the shooting script) could work without it. It possibly could even have been a good movie with the right support from producers and such. However it probably should not have been Blair's story, but it is what we got, and for that reason I hope you guys all are understanding that I usually approach this topic from that angle.
Sure the theatrical cut bare-bones Kilrathi invasion story could be told just fine without Pilgrims or Blair's abiliities, but that version of the movie's story would have needed a rewrite... or a different script altogether to flesh out everything in the absence of any character development, and to make the Kilrathi a real threat with some better explaining behind their motives. They shot a movie about Pilgrims and then tried to make it about a Kilrathi invasion in the editing room.
The movie script (at least in the original draft) does tend to channel Star Wars quite a bit though in general. As much as Wing Commander was inspired by WW2 it was also inspired by Star Wars. The comparisons aren't a mistake.
Wing Commander always felt more grounded in sci-fi compared to Star Wars being essentially a fantasy film set in space. People got upset that it seemed like the movie was trying to add space magic to a series that, up until that point, seemed to avoid anything that may have looked like it (though there was that time that Viking looking dude visited the Claw looking for an orb). This is the opposite problem people had with The Phantom Menace. People complained that Lucas was taking their space magic story and taking the magic out of it. However people weren't mad because midichlorians somehow made Luke special ahead of time. Luke was special because he was force sensitive regardless of whether it was space magic or space amoebas. This was already established many times by things Yoda and Obi-wan had said in the original trilogy. [Just as an aside, I will add that The Phantom Menace doesn't explicitly say that the midichlorians are the source of the force either. That actually would seem to contradict everything we're ever told about how the Force works, and how it's an energy that's present in every single living thing. It actually sounds like they are more some kind of symbiotic parasite that is found in high concentrations in people that are force sensitive, which gives the Jedi a convenient way to test if people would be a good candidate for Jedi training. ]
It likely would have been much better to not invite the comparison between WC and Star Wars in the first place. Even so, editing Blair's internal struggles out of the film only further served to emphasize his 'powers' when part of the point of the pilgrim plot is that Blair doesn't feel special and rejects the idea that he's special. The pilgrims felt they deserved to be treated special for it and there was a civil war where most of them were wiped out because of it.
Having Blair's abilities being genetics based doesn't change whether he's an 'everyman'. The disconnect for us fans is more as you mentioned that Blair was no longer my or your character. That's not so much an internal problem with the script or story being told though. That's more of the danger of adapting a game and sticking to the characters established in the game. How us fans of the games view the movie as opposed to how the movie stacks up as a stand alone piece of art (or entertainment) aren't the same at all. A movie even if it's decided it's somehow tied in to the game canon typically should have it's own internal consistency and be accessible to a broader audience. There's been a marked for more direct tie in films but usually those area direct to DVD or direct to digital tie ins of varying quality like some of the more recent final fantasy, or Mass Effect and Deadspace animated films. They usually have a really small budget and are sold almost exclusively to fans of the series.
Edited for clarity... I was in a rush when I originally wrote this, so, yeah, lets blame it on that.