Why are the shounen lead protagonists usually shown to be stupid? One Piece's Luffy, 
Naruto's Naruto, 
Fairy Tail's Natsu, 
Reborn's Tsuna, 
Dragon Ball's Goku 


All of the above are shown to be simple-minded and foolish. 

Why is it so common to depict the lead protagonist to be so stupid?
This is a common archetype in many forms of fiction, not just shounen anime and manga. for instance, many seinen romance series have protagonists who are usually at or below average intelligence, e.g. Clannad, Chobits, though seinen also has some intelligent protagonists like those from Death Note or Ghost in the Shell. Shoujo series also sometimes use this archetype. However, I suspect it is especially common in shounen series and other series targeted at children.

One reason for this is that if the protagonist frequently spends a lot of time deeply considering things, and comes up with complicated logical thinking to justify his actions, it can easily confuse some of the viewers, particularly younger children. In a mystery series, this might be acceptable, because the viewer is expecting to have to think critically to follow what's going on, but in an action series, it detracts from what most people are watching for.

Another reason is that for the protagonist to be a good hero (or arguably even a good antihero), they need to be identifiable to the average viewer. It's easy to identify with people who aren't as smart as you are, because at some point in your life you were like that. Since some of the viewers will be fairly young, to make this work you need to make the character at or below their intellectual level, which makes them appear really dumb considering their age. It's much harder to identify with someone who is far smarter than you. Extremely intelligent characters are supposed to be impressive rather than identifiable (e.g. Light and L from Death Note, who are identifiable in other ways, but not in terms of their  intelligence). Of course, it's also possible to just make the character average intelligence and not put any emphasis on that direction (and lots of series do this), but shounen protagonists tend to be more like caricatures than real people, i.e. they have exaggerated features and characteristics, and intelligence is often one of them.

It's also worth noting that most shounen action shows were, at least originally, marketed to young boys. Most young boys are far more interested in being strong than in being smart. By making the character below-average intelligence, but unbelievably strong, it makes the character simultaneously identifiable and admirable.

There's also the comedy aspect. Almost all of these series involve comedy. For whatever reason, many people find people doing stupid things to be funny. A lot of these series exploit this by making the protagonist almost useless outside of battle. In the traditional Manzai style of comedy, they play the boke role, which is usually the more interesting role (hence fitting of the protagonist). That isn't to say that intelligent characters can't be comical, but it isn't as easily exploitable with little-to-no effort as it is if the protagonist is unintelligent.

Finally, the protagonists in most of these series are idealists. Intelligence, by and large, correlates with pragmatism, at least in anime. Pragmatic characters make good generals, but typically not interesting ones. To put it a different way, pragmatism wins wars, but idealism leads to epic battles, and in an action series that's what counts. Dragon Ball wouldn't be nearly as interesting if Goku resorted to some form of guerrilla tactics to win each battle, even though it might make things easier. The protagonist usually has some more level-headed allies who will pull out if they really are in a losing battle (e.g. Nami, Piccolo), but these characters aren't the ones you're supposed to identify with. Also, idealism is often portrayed as admirable in these series, which further adds to the character's good qualities.

There's also the aspect of tradition, as kuwaly's answer points out. So I think there are a lot of reasons why it works well to have an idiot hero in shounen action series, so it's understandable why they are common.