Did you see the thread with the mock-up NX perhaps? That helped me picture it.

I did, I did, and that only made it worse because they look very uncomfortable.

I mean, why does a handheld (as the controllers will be used when working as that) need detachable controllers for multiplayer? Nintendo handhelds have been offering multiplayer experiences since the original Game Boy with the Game Link Cable without needing controllers.

For two players on one screen, or perhaps for motion control for one player on the portable screen or at home.  I expect Nintendo will want their back catelogue playable on this system, and that will require motion controls. 

Let me describe the picture that comes to my mind: two players (and just two, as there are only two controllers) want to play multiplayer "on the go" with a NX, so they take one controller each and leave the main unit with the screen somewhere between them so they can play without bother each other.

Now tell me, how big does the screen need to be to make this multiplayer thing useful and enjoyable? And would you really leave the main unit with the screen away from you, knowing that someone can cross and, not necessarily steal it, but simply get in the way or just hit it by accident with a bag and droping it to the ground?

Also, why would Nintendo design a machine with more points where it can break (the points where the controllers would attach to the main unit)? And why would they make a 180º change on their idea of multiplayer of "one game/as many machines as players" to one of "one game/one machine"? They are losing console sales going that route.

Why are you playing games when there are thieves and bag-swingers around?  You need to be aware of your surroundings. 

My niece plays tap games all the time with her iPad on the floor. She doesn't do this in back alleys or college hallways. 

But why would you need those detachable controllers to play at home, where an updated Wii U Pro Controller would do wonders? No, those detachable controllers are ment to be used when playing outside, usually in the street. And that brings the situation I described earlier.

So you ask why it would have detatchable controllers, I give you two examples, you say no and then say the reason is to play in the streets, which makes no sense.  I just did a quick google search of "playing with tablet".  Through 50 images I didn't find a single picture of someone playing with it in the street.  I saw people on the floor, in bed, on the couch, on a swing on their front step.  But never on the street.  The closest thing was on the beach after about 60 images.  The purpose of detatchable controllers is, most likely scenarios like this:

Where two people want to play a title but would rather not touch each other's hands all the time.  They could also be used if you want to play a game like Smooth Moves away from the TV using the detatchable Wii mote like controllers.  But there is no point in using them walking down the street, that is stupid so it pointless for you to suggest that's there purpose.

Tablets are used predominantly in the home, just away from the TV.  If you are using the device solo, on the train, you can just leave the controls in place and play your game of Breath of the Wild.

In how many of those images did you saw someone playing with a controller? Because we're not talking about a tablet or smartphone, we're talking about a console with controllers. Detachable controllers.

If you're going to use it at home you don't need them because there are better options (like proper controllers), and if you're going to play outside... how do you use them safely? That's my main concern about them.

But there's nothing to be "concerned" about.  You just leave them attached if it's not enhancing the game play.  If the NX is connected to the TV, it will most likely be using something like the Pro Controller and/or Wii Remote.  But this system needs to cater to the DS crowd as well - moreso really - and those gamers typcially play at home in a room, on a couch, or in other venues.  For these uses, Nintendo clearly sees a novel use for having the ability to remove the inputs.

Removal of side controls could also be centered around something else entirely.  Perhaps they want the system to go "full tablet" under some circumstances if the user just wants a tablet and not a true gaming system at times.  Or perhaps it is in connection with the recent pattent that showed various types of inputs being used and interchanged, such as buttons, analogue sticks, d-pads and NFC readers.  Perhaps it's not about using the controls detatched, but more about being able to "attach" changing methods of input.

Sorry but I still don't see any advantage. The only use I can see (more or less) is if the two controllers are like the two halves of a Pro controller and can be connected together to form a Pro controller to play on the TV. But that would make the design of the device with the controllers kind of odd.

And about having interchangeable bits... God, please no! Not only will they be selling Amiibo, but also gamepad add-ons?

*shudders*