Rock Paper Scissors won't work in D&D because Rock players will complain about Paper, Paper players will complain about Scissors, and Scissors players will complain about Rock. RPS accepts being strong in one area and weak in another area as balance. Those who don't like RPS want balance to mean everyone is equivalent. You can have your specialization where you're the Best at this Thing, but no one is helpless at another character's Thing he's Best at. For example, a major issue in 3E was people complaining about having a poor Will save. In 5E it's Wisdom save. Spells attacking that cause someone to Lose A Turn, effectively. People do not want to lose turns. They're fine with such spells existing, mostly, but refuse to accept anyone being weak against it. Let Enchanter be the Best at Lose A Turn spells, but no one may almost always Lose A Turn because of it. It's why people are always encouraged to take Resilient (WI) feat.

To clarify, D&D is certainly capable of having RPS rules and many players will likely enjoy it and be happy. The issue is there are enough players who won't like it and complain about it, it leaves doubt D&D did the right thing.

As a matter of personal opinion, I don't think I have a personal opinion on the matter. I'm more caring about the final result of the rules whatever they are rather than the philosophy of which version of balance is better. I don't worship balance. As an example I utterly reject the Tier System of 3E as a guidance for anything about 3E D&D. It was and only will ever be one person's personal opinion, not gospel.