Yes but the DMV is one of hundreds of government agencies. Personally, I've never had issues with the US Postal Service, it's always delivered my mail on time and never, ever lost a letter or package. SS admin gets out millions of payments on time, etc. For every example of an inefficient government agency, there is a well-run government agency providing good service delivery.
Meanwhile, there are any number of horribly run corporations that remain horribly run for long periods of time. Read up on the auto industry history if you don't believe me, for example.
My point is that such broad stereotypes aren't helpful for such important policy issues. That AND evidence that many countries that do have a publicly run health care system deliver better health outcomes at a lower cost than the US, so it seems that it is not axiomatic that public sector = worse than private sector or that public sector = poor quality/service delivery.