They tried to ban genres of comics back in the 1950s in America:
http://cbldf.org/comics-code-history-the-seal-of-approval/
They thought that comics were poor quality, encouraged bad reading habits and loss of moral purity with their pulpy themes about sexy people, monsters and crime. They galvanised puritans and parents everywhere, burned books and enforced a code on comics that they had to follow rules like "no werewolves" and "criminals must never be characterised as sympathetic or glamorous". It's the reason superheroes came to dominate the genre. It caused comics to become a children's medium for decades, removed all complexity from the genre and pushed out marginalised voices by making superheroes one of the only viable and profitable genres, leaving romance all but forgotten in graphic novels. It's basically why webcomics and sales of physical comics are now so dominated by romance in manga style; American comics shot themselves in the foot but the audience was still there, and when manga became available... well, that audience pounced on it!
Soooo.... no, I don't recommend it. People who want that kind of thing will just go where they can get it, so they'd just move to comics or fanfic or something and the places that banned it would just be poorer and reading advocates would be pissed because reading is good for people's critical thinking and emotional wellbeing, so it's better a person is reading than not reading, even if it's Twilight and not... I dunno what this person would consider "good", they sound like a pretentious asshat, so they probably claim they've actually read James Joyce's Ulysses (nobody has actually read this book, anyone who says they read it is LYING, I've written a decently scored university english lit essay on it and I've only read a quarter of it).
Honestly, hating on YA is basically just more of the usual hating on teenage girls. Romance has been the most popular genre of novels for... well, basically since novels became a thing. It we ban Twilight for being a story about a young woman torn between two attractive men... well, should we ban Pride and Prejudice as well? That's also about a young woman torn between two attractive men, after all!