Yes, district attorneys should be compelled to conduct such tests, but only when ordered to do so by an independent panel.
It would be ridiculous to require district attorneys to conduct tests every time a convicted criminal requests one. So many of the tests would be frivolous that it would be a huge waste of resources.
Equally, however, district attorneys should not have the power to decide which cases they will test. They will often tend to be biased against convicts, believing that their office could not have made a mistake. Therefore, requests should be submitted to an independent panel with authority to decide when such tests are warranted.