There appears to be no word more invasive in both critical and creative thought than the word "trope". It's a word I despise, a word that the users use with such regularity that it means nothing but cliche. The huge issue, I believe, that this word has is baggage. Mainly the baggage of the site that published it.
TV Tropes, as a website, is a piece of garbage. For proof, look at any of the real life tropes. Did you know that on the Trope page for Pistol Whipping, Matthew Sheppard is listed there? For more proof, look at their regular pages. Did you know that under a page about poorly written morals was "Twelve Years A Slave" with the caption "we get it, slavery is bad"? Really, that entire Tumblr is a good resource, immortalizing all the asininity of the site.
A different issue, entirely, is that there are too many pages with obscure Japanese names. It doesn't help the layman looking for examples on your Wiki if they need to know words like "Tsundere" and "Yandere". You do, however, get a chuckle if you're in the know- which is absurd (and this is coming from the guy who wrote about Yugioh characters).
The secondary, and more annoying, issue for me is the complacency the site breeds in writing. While the site refuses to be truly critical of any piece of media, swinging easy softballs and edgy pool tubes in the place of thought, TV Tropes by its very nature encourages the legoizing of writing. No longer do your characters need to serve a narrative purpose, they only need to fill a role and accomplish a checklist.
I've seen this myself in my time assisting people who are lesser at writing. It is far easier to make a checklist than it is a story. It is far easier to try and break down a singular work of fiction you enjoyed to constituent blocks than it is to expose yourself to new fiction that takes creative risks. It is far easier to try and fail to interrogate concepts any writer with any practice would find "elementary" than it is to practice.
Unfortunately for me, that's what I think whenever I see the word "trope". A connotation of laziness that emphasizes talent over skill follows the word. Which is what makes it so annoying to see in critical thought. How can amateurs write well if their starting source is a pile of garbage? The answer: They can't.