That was such a bad situation. The whole, "how dare you question me, get out," loss of Gates McFadden. Dr. Pulaski's introduction as Bones 2.0 instead of as a distinct, unique character, and her first comments to Data. I think Diana Muldaur is very talented and a Star Trek icon -- TOS and TNG. Pulaski is a strong character, but that first impression was hard for me to shake. I was happy when Dr. Crusher returned, but by then I was also also sad to see Dr. Pulaski go. I wish that PIC had made room for a Dr. Pulaski appearance.
You're not alone in that. Pretty much everyone I've ever encountered who dislikes Pulaski as character... it's because all they remember of her is that first scene.
She's a great example of just how brutally important first-impressions are.
I definitely disagree that she wasn't her own, distinct character -- she was, I think you're letting that bad first impression continue to color your perspective. It's easy to misremember Pulaski as being abrasive and antagonistic because of that first scene, and hard to remember that she apologized very quickly after that, and very quickly became friends with Data (and remained very supportive of him throughout her time on the ship).
So it's weird seeing so much of the "discourse" on Pulaski boiling down to fans being angry at her for being mean to Data that one time while conveniently forgetting that she was one of only two people on that whole ship who went out and befriended the Android.
I was glad to see that Pulaski at got a tribute with a ship named after her in PIC Season 3. That at least implies that she went on to do great things after leaving the Enterprise. I like to think that the USS Pulaski was one of the last to succumb on Frontier Day because its crew had the oldest combined age of any ship in the fleet.
That is a fundamental misunderstanding of how transporters function in the Trek universe. There is no destruction, duplication, and recreation of objects. Matter is simply converted into quantum information and then converted back.