I do not know the details of the laws in the four states (so far) refusing to recognize Tennessee driver's licenses. My guess is if they don't recognize TN licenses as valid, they could technically consider you are driving without a license. There is a federal issue regarding interstate travel which might come into play. The federal government could intervene and say that a license "war between the states" might violate Section 1 of Article IV of the U.S. constitution regarding "Full faith and credit shall be given in each state to the public acts, records, and judicial proceedings of every other state...."
Commercial Drivers License (CDL) requirements are more stringent. I have one issued in Tennessee and had to take comprehensive written and driving tests which I do not think would be considered invalid by other states.
There is a federal issue regarding interstate travel which might come into play. I remember being told in school, or possibly drivers training, that if you were subject to a states 'higher fine schedule' for out-of-state drivers, you could submit the ticket to your congressman for payment (reimbursement).
Not that I 'believe' it would be so easy...
but it would seem to be jailed etc by another state for having a Tenn. DL, you would have a decent court case if not some venue of recouping your losses by going to US GOV.