Michigan Drivers Responsibility Fees are routinely discharged in Chapter 7 and Chapter 13. However, there is an exception to discharge for debt that is "a fine, penalty, or forfeiture payable to and for the benefit of a governmental unit, and is not compensation for actual pecuniary loss." 11 USC 523(a)(7). I believe the nature of these fees are monetary sanctions. In other words, they seem to be punitive in nature and not compensating for an actual pecuniary loss.
My interpretation of the Bankruptcy Code is that these fees should survive a Chapter 7 bankruptcy discharge (Section 523(a)(7) is a self-executing exception to discharge, so no adversary proceeding is needed). Section 1328 of the Bankruptcy Codes, which governs what is discharged in Chapter 13, does not include the 523(a)(7) exception to discharge. So, these fees are discharged in Chapter 13. The State is fully aware of the 523(a)(7) exception to discharge. They use it all the time for statutory fines related to overpayment of unemployment benefits. It may be that they've made a policy decision to allow these debts to be discharged/eliminated in their records when a person files Chapter 7.
Chapter 7 may work, it may not. Chapter 13 is definitely the route to go if you're not willing to take any chances in getting rid of Michigan Drivers Responsibility Fees. In all cases, a person overwhelmed with debt should consult with an experienced bankruptcy attorney. An experienced bankruptcy attorney should be able to evaluate your situation and help you decide the best way to get the relief you need.