In essence we already have the practical version of that. If someone is convicted of a crime punishable by more than a year's imprisonment, even if they are not sentenced for that length, they become a legally prohibited person.

But people are arrested for DUIs and have the charges dropped for lack of evidence all the time, to deny a legally innocent person the exercise of a fundamental right based merely on arrest, without any due process, is not "reasonable." 

The only reason revoking a person's license for misdemeanor mala prohibita DUI convictions passes either state or Fed Constitutional scrutiny is because driving is legally considered a privilege, not a right. Given that possession is the core of the RKBA, and statistically very few people ever convicted, much less arrested, for a DUI, particularly a first and only offense, ever go on to commit other crimes, there's no way that would pass Constitutional muster. 

It's a Right, that's the starting point for discussion.