I remember Star Wars, and you're greatly exaggerating.
Luke playing with a toy ship means jack shit. I had a LEGO spaceship as a kid, doesn't make me a fucking astronaut.
What does him joining the Academy prove? We have zero information on what the requirements are to join, and for all we know Luke could want to be joining the academy to learn to fly. You know, learning, something academies kinda exist for.
Luke tells Han "'I'm not such a bad pilot myself". We've given zero context to this, it's something Luke says out of nowhere and Obi-Wan stops him from elaborating. Piloting what exactly? Not all ships operate the same and also Luke's cockiness is apparent in the first movie. I have no reason to take much stock in this random claim.
His claim at being able to fly something like the Falcon loses a lot of validity when he proves how ignorant he is on how hyperspace works when Luke seems to not understand why Han isn't just immediately going to lightspeed and Han explains that just jumping into it without a set course could easily get them killed (actually, the odds of this happening in reality are very slim given the vastness of space and how all objects ultimately make up an insignificant portion of its mass, but by the movie's argument Han is supposed to be in the right here)
Finally, mere minutes before the final battle, Luke finally provides more clarification by mentioning hitting womp rats in his T-16 back home. Again, not much to go on here. The movie has not identified what a T-16 is up to this point, yes Luke has a toy of one but it's never identified by name. For all I know up this point in the movie, a T-16 is Luke's flying car that actually had a weapon somewhere, I mean that's the only sort of vehicle he had been seen operating up to this point in the film. Is it capable of leaving the planet or is it purely a land fighter? Does it handle similarly to a X-Wing? Has Luke ever flown with others and knows how to avoid accidental collision?
None of these things are elaborated on, and Luke being able to pilot anything at all is only given real merit mere minutes before he actually do so. That's terrible set-up, especially since Luke's flying skills help resolve the entire conflict of the movie.
Imagine a fantasy movie where the heroes approach the villain's castle in the final act, and this exchange occured:
Hero dude: All right, people, Count Asshole's lair stands before us! I know our odds are slim as his fighting prowess is unparalleled and his speed is beyond any mortal's, but still, we must persevere and-
Best friend: Actually, I have a magic spell that can greatly lower his speed which will improve our odds quite a bit.
Hero dude: What?! Why didn't you mention this before?!
Best friend: But I did mention it.
Comic relief: All you said was you know a bit of magic, you didn't specify anything at all or ever use any magic at all up to this point. In fact, you even showed ignorance in using magic at one time!
Actual magician: Yeah, you asked me why I was focusing before using a flame spell! If you were good at magic, how did you not know that casting fire without first focusing for a few seconds would simply cause me to burn alive myself?!
Bard: And you're making my job very difficult! So in my story, we're about to face the villain with the odds badly against us, and you pull this out of your ass?! My audience is going to call bullshit!
Best friend: But I vaguely alluded to it once with zero context or proof, isn't that enough?
Hero dude: No, and as punishment I'm going to tell you that girl you've been making googly eyes with is your sister.
Bard: Oh come on, now people will just think I'm making this story up as I go along!
Hero dude: Naw, it's cool, they'll think you had everything planned out even though you didn't.
Now is Rey being familiar with the Falcon also only clarified mere moments before flying it? Yes. However, there's a VAST difference between using a spaceship to take out a total of TWO TIE fighters, and using a spaceship to win the entire battle of your movie. The former is problematic but doesn't ultimately affect the larger conflict by any noticeable degree, and the latter, well, RESOLVES THE ENTIRE CONFLICT OF THE FILM. A New Hope should have done a better job of establishing Luke was A) a good pilot, and B) could pilot something similar to a X-wing. The movie does not do either of these things.
On another note, how the fuck did Luke manage to nail a bunch of stormtroopers and a small control panel from a great distance before they got in the Falcon to leave the Death Star? There is zero reason to believe he's ever used a blaster prior to the movie's events, how the fuck did he nail that many shots at once? And if you say, "Force sensitivity improves physical traits!", well, a bunch of complaints towards Rey's skills are now easily dismissed by that logic.