@Inna22, whilst I would agree that the provision of ID from Guests can greatly help to provide Hosts with more than a little bit of "security", a Guest having and supplying an ID is no guarantee that all will be 100% well by the time they depart.
Equally, someone without an ID, isn't necessarily going to leave one's place in a mess, remove items, or otherwise defraud a Host.
If Airbnb doesn't insist upon an ID for every Guest who stays at your place, then in order to protect oneself, I would imagine that the only thing to do - BEFORE anyone actually books - is to add wording to your listing to state that no booking will be accepted in the absence of an ID.
As to what this Guest may or may not have done in the past, whilst we're all entitled to our own opinions, and decisions as to what best to do, "We" are not in possession of the facts of what they did or didn't do, and therefore we would be as morally wrong (in my opinion) to determine Guilt or Innocence upon someone we've never met, who's never stayed with us, and who - irrespective of our own, and/or others' opinions of the case against the person - under most Countries' legal systems - are considered to be innocent until proven guilty (and NOT the other way about).
If one doesn't feel safe/secure about the Guest, then the option to Cancel the booking remains with the Host.
In this instance I would imagine that if the Host requested cancellation via Airbnb support, it is highly likely that the latter wouldn't accept the reason provided, as it might well be deemed to be discrimination.
