I don’t inherently dislike the use of the word “perplexing,” but I DO have problems with charts like the post you are referencing.
commonly I see “references for writers!!” “how to make your writing more interesting!!” “all writers need this chart” posts and it’s just a mile long list of words that are multisyllabic synonyms for things that could have been said in a more succinct, less awkward way.
it leads new writers to thinking that they need to look for different words that mean “mad” (and if they are getting real fancy, words that mean a certain type of mad) to make their work better.
however, more often than not these writers work with creative fiction, and that line of thinking leads to very clunky, painful writing. want a professional example? pick up a stephanie meyer novel. she does this all the time (think the rather humorous list of all the ridiculous ways she replaced “said” in her dialogue tags in twilight).
so yeah. perplexed isn’t bad. in a academic paper it could fit, or in a work with a humorous tone it would do nicely. it could be GREAT in poetry, and I would suggest it if you have a character that’s a pompous asshole speaking. but do I think it would be in a drop down chart of words that “every writer needs to know”??? absolutely not.
in fact, the concept of a master list words EVERY writer needs /in itself/ perplexes me.