You are saying, when you turn on for the first time a dag with e.g. @daily schedule, and catchup = False, if start date is 2010-01-01, then it would run first the 2010-01-01 run, then the current run (whatever yesterday is)? That sounds familiar.
Yeah I don't like that behavior. I agree that, as you say, it's not the intuitive behavior. Seems it could reasonably be categorized as a bug. I'd prefer we just "fix" it rather than making it configurable. But some might have concerns re backcompat. What do others think?