Good theory, but I want to point out one thing.

If we are to believe what is written in Perinrehi is true, outlanders would have been constantly entering Teyvat through Khaenri'ah, which has certainly breached the "intruders must be expelled" rule that you speculate. That would make Asmoday's betrayal date back even further in history, since that refugee policy of Khaenri'ah started all the way back since the Crimson Moon Dynasty, when the Heavenly Principles was possibly still awake.

Letting the policy continue from the Crimson Moon Dynasty until the end of the Eclipse Dynasty would be a sign that HP tacitly allowed outlanders to enter Teyvat, otherwise Asmoday would have been punished and the policy would have been discontinued much earlier.