To be mindless is to not be mindful. But it is entirely possible to mindfully pursue something mindless. A good example would be looking at photographs of cute animals. It is with complete mindfullness that I am giving myself the sugary buzz that comes with this activity. But here is the dilemma, there is absolutely nothing INTELLECTUAL about this and so one could say it's a waste time. Possibly, yes. But surely, mindlessness is fine as long as you're really paying attention to the act at hand, and making note of how you feel in a MINDFUL way.
Therefore the conscious pursuit of something mindless is a worthwhile endeavor.
Repeat after me:
"I am in the present moment, the here and now. I am looking at a napping baby koala. And I feel wonderful."