Those "smart" dumb phones still are stuck on the "dumb" internet called i-mode which is basically a slightly less sucky WAP internet but still a walled garden and not the real internet. The Japanese have recognized the advantages of actual smart phones with actual internet access and the flexibility of the touch screen interface.
Not true. Many (most?) phones have a full browser. My keitai in 2006 had that, along with stuff like support for reading office suite and PDF documents. Full Web browsing isn't new to Japanese mobile phones.
There's a long list of features that Japanese keitai (mobile phones) have that the iPhone doesn't. A couple examples are support for QR code, Suica/Felica, and one-seg.
QR code is a form of barcode that can be printed in magazines, newspapers, on billboards (aboard trains, for example), and so on. Point your phone at the QR code, press a button to scan, and you instantly have all the relevant information (phone number, Web address, e-mail address, etc.) (Yes, there are some iPhone apps that can process QR code using the camera and usually some remote processing, but that's crude in comparison and costs extra.)
Suica, Felica, etc. are contactless payment cards embedded in the phones. Stop by the convenience store, wave your phone at the register, and you've paid for your Pocari (or whatever). Same with entering train stations.
One-seg is the free mobile digital television service. It doesn't work underground, but it does work aboard above-ground commuter trains and (of course) while stationary. You can watch your favorite baseball game, for example, free. (Initially the mobile carriers resisted implementing this feature since it wasn't a revenue generator, but now it's quite common.)
The iPhone supports none of these features, and many Japanese like them and want them.
I also agree with the other posters explaining that dedicated keypads work very well for Japanese text entry. It just takes longer to enter Japanese text on an iPhone soft keyboard.
This is going to sound silly, but it really is true: Japanese keitai have a place to attach straps. The straps are fashion accessories for both men and women, and they're very important. The iPhone doesn't have that, so it's not very convenient to attach straps with all those little bits of jewelry and other things.
And I could go on and on. The Japanese mobile phone market is quite special and different.