Twilight Sparkle is my favorite out of the Mane 6, so I'll try my best to explain why I like her and bring up your points. Twilight has been the main character of this show from the very start, so a heavier focus on her opposed to the other characters is to be expected. However, that's not to say that the other character's don't get focus; I personally think the focus of the characters in each episode is pretty balanced. I've never felt that one character was getting too many or too little episodes.
Anyway, this show is still mainly about Twilight learning about friendship. In the beginning, Twilight is shown to be a very anti-social Pony who does not have any interest in becoming friends with other ponies, and is even a bit rude. However, she does develop throughout the show and learns the value of friendship bit by bit. Like others have said, Twilight Sparkle can be very relatable to some, so it is very satisfying to see a character like you rise to greatness. Becoming the princess of friendship makes sense for Twilight due to the whole show prior to Magical Mystery Cure revolving around her learning the lessons. Her ascension is essentially a graduation for her friendship lessons.
Another good thing to point out is that her journey there wasn't rushed either. She had to learn many lessons, showed that she wasn't perfect many times; one notable example being her behavior in Lesson Zero. As for her being overly privileged, her special talent is specializing in magic, so it makes sense for her to have Princess Celestia give her special lessons and education. Studying magic relates directly with her talent. Same thing with other characters. Rainbow Dash is able to attend the academy for the Wonderbolts, which is presumably pretty hard to get into, let alone do well. And I've never seen anyone criticize Rainbow Dash for that.
Back on topic, Twilight Sparkle wasn't handed her gifts either. She is shown throughout the earlier seasons practicing her magic (e.g. teleporting, transmutation, etc.), so she did have to work for what she has now. She also has been shown to have her head in a book very often, so it also makes sense for her to be as intelligent as she is. That's just a part of her character.
Now for her character post-ascension. The fourth season was mainly dedicated to her adjusting to being an alicorn princess. Not once did I feel she became too comfortable too quickly (and to be fair, I still don't think she's entirely adjusted yet, which is a good thing). It was crucial for the writers to make sure they put a good focus on Twilight so her new status makes sense for the show and the character. However, this does mean that there would need to be a higher focus on Twilight Sparkle, which did happen in the fourth season, but I don't think she received too much focus. The other characters still had their chance to shine (and if you look at the episodes, Twilight actually doesn't have that many episodes that focus on just her).
Finally, the fifth season. Twilight Sparkle actually has had very little focus in this season so far. She has adjusted a bit more into her new role as princess of friendship, which gives a little more room to focus on the other characters. The premiere had a very high focus on Fluttershy and the townsfolk, Castle Sweet Castle focused on the Mane 6 as a whole, Bloom & Gloom focused on Apple Bloom, Tanks For The Memories on Rainbow Dash, Appleoosa's Most Wanted on the Cutie Mark Crusaders, Make New Friends but Keep Discord on Discord, and finally; The Lost Treasure of Griffonstone on Pinkie Pie, Rainbow Dash, and Gilda. As you can see, not a single episode has solely focused on Twilight Sparkle.
Now, those are the main reasons why I disagree with your viewpoints. As for why I like her as a character, I personally find her to be the most satisfying to watch and grow, and she has a very relatable personality for me. This is why she's my favorite out of the Mane 6.