Should States provide free government issued IDs to voters?

Absolutely, and many states do. That, however, will not make any difference to the "anti-voter ID" folks whose primary reason for not requiring ID is to ensure continued voter fraud to get their liberal candidates elected. Nobody should be allowed to vote without proof of voter registration and proof of identity. There is simply no valid reason to not require ID.

NC has a voter ID law and issues free IDs through the DMV.

Absolutely. By all accounts, we have a lot of aliens residing in the United States, many undocumented/unregistered. Many with agendas inimical to the vital interests of the country. Without IDs that prove citizenship, we are allowing them to interfere in the expression of the will of We the People. Sadly, we don't have a trustworthy form of identification. California, for example, is handing out valid drivers licenses to illegal aliens like condoms at a whorehouse. Illegal aliens also have bank accounts and rent residences and can produce valid utility bills and bank accounts. Thus, it's not a matter of "if" but rather of "how".