Can I have an ID card that is JUST and ID card, with a driver's license that is a separate piece of paper/plastic?
When I present my ID card to cash a check, clear airport security, etc. it's none of anyone's business if I have a driver's license.
After all, other government-issued licenses like concealed-handgun permits, hunting permits, and professional licenses (engineering, medical, etc.) typically aren't on the same piece of plastic as your state-issued ID card. My bank doesn't know or care if I have (or don't have) a gun permit, a fishing license, or an license to practice medicine, and that's A Good Thing.
Splitting the driver's license from the ID card would also be good for military families and college students who didn't have a previous driver's license but who want to keep their "legal residence" where they previously lived - it would allow the state where they actually live to issue them a driver's license (valid in all 50 states) without either forcing them to surrender their existing ID card or giving them a second state-issued ID card whose information (address, etc.) may conflict with the existing card.
It would also solve much of the "short-term visa/expired visa/illegal immigrant" problem at least with respect to immigrants who still possess a valid, recognized non-US-government-issued ID card such as one issued by a foreign Consulate: States would be able to ensure that people who are driving can pass a driver's test, are paying the appropriate drivers-license-related taxes/fees, and are properly insured without having to face the political heat that comes with issuing an official ID card that is valid for purposes other than proving you are legally qualified to drive. If "political heat" is a concern, the document can be stamped "Valid as a driver's license only. Not valid for any other reason. Only valid on days in which the person has a legal right to be in the United States of America [this is for frequent tourists who use non-contiguous successive short-term visas but who want to pay for a multi-year driver's license]. While driving licensee must posses a valid government-issued photo ID card recognized by the United States, the state of [state issuing the driver's license], or the state in which the person is operating a motor vehicle. Licensees not possessing ID cards issued by the US government or a US state government must possess a valid travel or residency document or proof of an exemption [e.g. an ID card issued by a government with a no-visa treaty with the United States] while driving. Not valid after [expiration date]."