In answer to the question are mashed potatoes a big deal in the US, especially at Thanksgiving, the answer is an absolute yes, but there are qualifiers. Generic mashed potatoes are mere side dishes. I find instant mashed potatoes an abomination (but some love them.)
What makes mashed potatoes a big deal is the occasion and they way they are prepared on special occasions. I truly look forward to the mashed potatoes and gravy more than the turkey at Thanksgiving. What is funny, every family has their own way that is mandatory. We LOVE lumpy mashed potatoes especially with some skin in the mix. I had always heard you should never have lumps. One year I didn't stir long enough, had lumps and loved it. Special occasions tend to mean special gravy which makes the dish delicious.
Not long after World War II, I had potatoes in England, and they were a different dish than in America, so that may be part of the difference. On whether potatoes can be a big deal, I bet if you tried to take an Englishman's chips away from his fish and chips meal, you would have a fight.
Making perfect mashed potatoes is an art. I'm not able to do it, but my daughter is wonderful at it. She uses a professional-grade mixer.
On the other hand, a glob of mashed potatoes in a cafeteria line, no thank you.
I remember the first time at the relatively old age of 12 I ever was asked to eat the skin. It sounded absurd to me, but I instantly loved it. It wasn't until the 70's and 80's that skin got to be popular. Now it's a treasured side dish by itself...just skin.....usually filled with cheese and butter.