No smoking in POH

I’m really asking too much here, aren’t I? One unit cleaned up exceptionally nice with new carpet, paint, etc. Two minutes in the unit and my clothes smell after I leave. I can smell the smoke outside.

As a non-smoker, I don’t think highly of the life choice to smoke. But I’m really asking for too much of tenants, aren’t I?

I don’t think you are asking too much at all. Landlords set rules and often do not allow pets, smokers etc. It 's your house and you set the rules.
When you screen for non smokers check their cars for cigarette smell.
Make it clear that you will not tolerate smokers and if you rent to someone let them know you will evict if you smell smoke in the home.