It's not so much that I find the idea of turn order in combat feel weird. But it does feel like when the discussion comes up, it seems like it's about combat. So I'm just curious about combat in RPGs that makes it a point of contention.
My first RPG experience is with DND 5e. When I first started DND, I actually thought it was really weird and confusing that there was no turn order outside of combat, and for that reason alone, I preferred DND sessions with combat. In fact, most RPGs I have played outside of DND have fixed turn orders, like A Quiet Year.