If I may take a moment to try to clarify where this bit of inane trivia comes from, it refers to a terrible misunderstanding of the prefrontal cortex. The PFC makes up around 12ish percent of the average human's total neuromass, and is the section of the brain most concerned with being 'you'...which is to say, 'you', your sense of self and consciousness. In this regard 'you' only takes about ten percent or so of your brain's run time at any given moment.
The gross misapprehension is that the rest of your brain isn't doing anything, which is absurd...the rest of your brain is extremely busy gathering and processing data into forms 'you' can collate, process and make decisions about, as well as running the myriad complex autonomic processes that keep you and your sensory apparatus alive to do so.
If 'you' used more of your brain, you would begin to lose critical functionality in every other area of your body which would rapidly render the whole exercise anywhere from futile to self destructive. Your brain is, in fact, a very busy place and 'you' has already been given quite a bit of room to work with.
This is, of course, still a very stripped down discussion of the subject. I encourage you to take your 'you' and your sensory apparatus to your public library analog of choice and read up on the subject yourself.
That aside, to answer the OP's question anyway, one must understand another fallacy of the brain. We have long labored under the idea that the brain was a fountain of infinite thought...that thinking about something costs one nothing, and that thus the only thing separating the stupid from the intelligent was the degree to which they cared to think at all.
In truth, as a physical asset, the brain is as finite in it's function as any other organ. Firing neurons takes energy...small amounts to be sure, at least individually, but it turns out that the brain is overall enormously power hungry (taking up around 20% of our resting metabolism) and a significant factor in our addiction to fast-burning sugars. Thinking too much can leave one as exhausted as any other physical activity, and at least if you've gone for a jog you've gotten somewhere and fortified your heart (which is, incidentally, also good for your brain).
So, what's so great about being stupid? Well, it's easier on the metabolism for starters, and leaves one feeling otherwise more energetic and able to deal with and enjoy the simple things in life without over-thinking them.
I wouldn't advocate being stupid as a matter of course, but it must be understood that a resting state is as necessary to one's mental health as one's physical.
I think you will find, at the end of the day, that those you perceive as stupid are actually quite mentally agile in the milieu of things they actually think about.