For the most part, I am ineligible for State ID/licenses--those are for 'residents'. However, though it may be possible to obtain one as a matter of emergency, IMHO it would give rise to undesirable presumptions. So I have avoided such.
I am for good order throughout my land. As for crimes/cases, it is important to settle those matters before attempting to 'retire' from the system. As for filing documents, if you happen to be an exempt foreign person it can be helpful to let Treasury know. The State license/ID open up a different door than the IRS tax file--those tend to have something to do with a State Attorney General or a Director of Revenue. However, Treasury now handles state-level debts too. I never did any of that birth certificate A4V paperwork--for lack of a "birth certificate" with my name on it, how can I? I do recall that may I have sent a certificate of foreign status (in connection with 1099 contract work, the company as Treasury agent sent the document to treasury--and no, it was not for Federal employment) to Treasury back in say, 1993. Never had any problems with them.