I'm sorry reading comprehension is an issue for you. You deliberately conflated two separate statements with no common reference. Probably just so you could get all righteous and post this.

we had classless urban environments inhabiting hundreds of thousands without any evidence of hierarchy or top -down management

Name 3. I dare you.

The 'owner class before writing' and European nobility are separated by time but not by nature.

The reason I say this is that when writing was becoming established, it contained historical events that were part of the oral culture of the time. We have records of behaviors of the oldest of cultures that already establish a noble and sometimes royal class that pre-existed the oldest extant documents we have.

Anthropological evidence shows legacy-based class separation as early as the beginning of agriculture and domestication.

My own opinion is it started around 600BCE when coin was used to pay armies for violent conquest

That's nice. You are entitled to your opinion. Ask your archaeologist mate the ages of the oldest decorated burials and then ask them if every burial in that culture was treated the same way or only certain people that also included valuable grave goods while everyone else was bare graves or even mass graves. Class separation has existed significantly longer than 600bce.

You aren't here for a conversation, you are just here to muddy the conversation so I'm blocking you now and forgetting you ever existed.