He also wants us to fulfill the ultimate purpose of creation, Yemos Hamoshiach, when He will be revealed to all, and everyone will serve him, and all of Torah will be applicable.
That’s His job. Our job is to follow the Torah.
Of course the concept of Moshiach, and iur belief in his coming, is universal. The obsession with it isn’t.
My daughter was in camp, and met girls from a Chabad camp. They were discussing the camp themes for the summer. When my daughter told them what their theme was (I forgot what it was), the Chabad girls gave her a puzzled look and asked, “What does that have to do with Moshiach?”
So yes, we say Ani Ma’amin, and daven multiple times a day for Moshiach,band yearn for the day when umol’oh ha’aretz deoh es Hashem, but it’s not to the exclusion of everything else in Yiddishkeit the way it seems to be in Chabad.
If you think that level of obsession is universal, you need to see other Yidden more often.