Generally? Well within the executive power / administrative law of any given state as noted by BlueFalcon below.
Practically? I’d expect it to be quite a struggle. For licensed professions in general (doctors, real estate, insurance, hairdressers, etc.) most or all states ask a question to the effect of “Has your license for profession ever been suspended or revoked in any other state?”. It may or may not be an automatic disqualifier, but even if not it’s an uphill battle.
It prevents the real estate agent who stole someone’s earnest money from upping stakes to the next state and getting licensed, but since the standards for suspending/revoking licenses vary widely by state I lean towards believing that perhaps it should be a factor, and perhaps the state board of profession should meet to review the application, but previous disciplinary action in some other state is in no way an absolute statement about someone’s fitness to practice in their chosen field.