Actually that's only part of their intended use. The data is also used to collect tax (registration) and maintain records of ownership (titling).
Many states also use this information to register, or solicit the individual to register, to vote. Law enforcement also uses this data for enforcing all manners of law when they look up a person to question or cite, not just immigration. Since drivers' licenses are used for identification, you can see that they are used on many government forms such as tax returns or background checks. Along these lines, the only way to ensure the government will not use your data would be to prevent the government from collecting and storing it (rough paraphrase from Snowden). But if you prevent the collection of the basic data referenced in the article, then how do you provide the same benefits to society that the systems do today?
The issues you have seem not to be about the state releasing records but rather with how the government uses the data. The basic information referenced in the article is also available in other country's systems to many of the same organizations authorized under the DPPA. Given the system is also about titling and registration, the access by debt collectors would be warranted, especially if it is dealing with a vehicle. How exactly is this system enabling stalking given the protections of the DPPA?
Do you have any examples of countries that don't aggregate data for government use and don't allow PIs to search many kinds of official documents? What system do you see that would replace the current one and maintain all the societal benefits but somehow increase privacy?