I'm a native speaker. "Égalité Irrefléchie" sounds ankward. I preffer "Égalitarisme irréfléchi" (back to male gender by the way). The first would be "thoughtless equality", while my version would be "thoughtless egalitarianism". But frankly, neither sound very good.

We have an approaching idiomatic term however: "Nivellement par le bas". Which quite literally means achieving equality by lowering upper bounds instead of raising the lower ones. It calls the image of cutting mountains off instead of filling the valleys. This expression is widely used as an applause light when talking about schools. (Generally, it goes like: "Let's help failing children in such and such way", then "But that method will slow everyone else down! That's a nivellement par le bas!")

(Oh, and please don't forget the diacritic in Égalitarisme or "Égalité". French typography requires it)