I don't think that's enough to explain the epic fail that is this design. It's more than just the lack of a hinge. I can't think of a worse handheld design in the history of gaming.
1. I don't have any hard evidence, but if you do a search for "broken DS" or "broken 3DS" on eBay, an overwhelming majority of them are on there by reason of "broken hinge"
2. As to why not make a sturdier hinge, the other part of this particular console is to bring the 3DS down into a cheaper price range in time for Pokemon-- which is why they additionally stripped it of the 3D and replaced the stereo speaker with a mono one.
I'm not personally a fan of the design, but in the short amount of time since it's been announced, I've seen a pretty impressive number of "I'd buy that"s from people on various forums, so I don't think this is as much of an "epic fail" as you think it is. Don't confuse "bad design" with "not marketed towards me".
Remember how a kid works; they start by treating it gingerly, then getting progressively more careless as long as it doesn't seem to hurt anything. A stronger hinge just means that they get to be slightly more careless before it breaks.
"I can't think of a worse handheld design in the history of gaming."
Not... really, no. The N-Gage required you to remove the battery compartment to change games. The Virtual Boy... well, pretty much everything about the Virtual Boy. The Sega Nomad, as neat an idea as it was, chewed through batteries in two hours, making it a handheld system in name only. You can get some other entertaining examples out of the big names, too.