The Andorians have played an increasingly prominent part of the franchise since then, with Jeffrey Combs’ Shran becoming a fan-favorite member of this race on Enterprise.
While the helmet designers didn’t explicitly mention this, they were most likely taking their Andorian design cues more from The Original Series than Enterprise because Discovery is meant to initially take place about 10 years before the adventures of Captain Kirk. In this way, the design was simultaneously inspired by the earliest Star Trek adventures as well as a very recognizable anime style.