It only protects a government employee who makes a discretionary decision as part of their normal duties. This might mean they get it wrong, but if they can show their decision was reasonable and (where relevant) pursuant to a process established by the agency, that's fine. In that case, the problem is the process not the employee, and so the proper defendant is the agency not the employee that is simply following procedures set forth by the agency.
Because that's basically what you're saying you want.
And anyways, if the DMV agent was acting in their capacity as a DMV employee and following established procedure, the DMV would end up paying their legal costs and settlements against the employee anyways...but without getting a say in the defense against the underlying lawsuit.
DMV agents are probably not very wealthy. By suing them you would simply drive an underpaid worker into bankruptcy and probably never get much money back.
Meanwhile, the DMV can easily scapegoat it's employee and never reform or make any systematic changes. Furthermore you would have no recourse to sue them directly since they can just keep hiring more poor workers to be thrown under the bus.
Ultimately the tax payers (or voters) need to keep the DMV accountable. There is no alternative. Democracy doesn't have shortcuts. The tax payers have to pay when the government screws up. More to the point - the tax payer ALWAYS ends up paying when the government screws up, without exception, 100% of the time. Either they pay by having a corrupt DMV that hurts society and everyone at large, or they pay through lawsuits and higher costs at the DMV.