There is some truth that having more practice with fine dining aids in better distinguishing flavours and textures, but most of it has to do with practice in identifying what Other Important People Tell You are desirable qualities. For example, in identifying fine wine, the average, untrained population cannot, study after study has shown, discriminate. One study(1) even showed that perceived quality and neurological response could be manipulated by simply mislabelling bottle price, regardless of actual price.
Should you like or dislike food because of what someone else told you to think? Maybe being told what to think is a sign of inept judgement and a lack of resolve--a different interpretation of having a "sophisticated palate."
Besides, different qualities--textures being particularly notable--can be desirable in one culture and entirely undesirable in another.
My advice: Just enjoy what you like and explore whichever foods you so desire. Take time to really absorb the quality of the food, and try out reasonably priced family owned restaurants. Stop reading the NYT to tell you what to think.
Particularly ridiculous addendum: This critic ordered, in the review in question, gluten free noodles even though less than 1% of the world's population has Celiac disease. If I went to work and addressed the problem I was given by tailoring it to 1% of my clients, I would be fired for being an idiot. Probably you would, too.
1) https://www.gsb.stanford.edu/insights/baba-shiv-how-wines-pr...