Maybe it's the other way around. Maybe the phone is not a text input device because it sucks at doing the job right.
Screen size is big enough. Capacity is more than big enough. There's plenty a reason to type on your phone. I, for example would love to do that while I take a longer ride in an intercity bus or car (as a passenger, don't get any ideas), or even while traveling by train (I'm a failed writer of sorts). I tried writing by hand in a paper notebook, but my scribbles look awful because I'm in a moving vehicle which constantly exerts forces (small but not negligible) so writing by hand becomes difficult.
For the classic writing style I need a hard place to put my notebook on, stability and a comfortable position, none of which are available while traveling. But a phone would do the job a lot better. "Get a laptop" you'd say, but with bigger size, smaller battery life span and no good place to put it on (except own lap) it's still worse than a phone.
Bluetooth keyboards are worse than a slide-out keyboard because they're not attached to the phone and eat up battery.
Another reason is IM conversations while traveling. They don't bother other passengers like talking on the phone does, you can do it with multiple people at once, doesn't really eat up bandwidth.
Yes, a cheap phone would do just fine but then I'd have to carry two devices which makes no sense.
I understand this particular case doesn't represent "a market" but there might be a market if such a device existed.
About cost: I guess the extra cost would be negated if companies would simply stop spending time and money creating all that stupid bloatware they push on the damn phones.