I have an Android tablet (which I'm using right now to enter this post) and an iPad. I've had both for years and I've done some development for them.
People DO use these things to be productive, but they are the exception rather than the norm. Part of the challenge is that even five years in our whole thinking about what an application should be has been shaped by thirty years of desktop and laptop devices. Anything that truly needs a keyboard (like writing this post) becomes cumbersome, even with something like Swype or SwiftKey. Pens suck, unless you're using a tablet with proper pen support (Note devices are great for this) but even then, most people don't currently need a pen.
It's not just the touch thing, though. It's really, really hard to build a good UI for a powerful app, even on a LARGE screen. To do so on a small screen without eliminating "power" features is almost impossible. And those power features are what people really need for productive work. They might only need 10% of them, but if the one they need is missing, that work has to wait until they can get to a larger device.
I don't think this is incurable, but it's hard to argue that writing a long essay on a 10" touch screen with no hardware keyboard is fun. I know people who use an 11" MacBook Air as their primary coding platform, but I know that I'm far more productive sitting at a desk with a properly-sized monitor and keyboard. (My MacBook Pro plugs in to those things if I have to use it for any extended period.)
Productivity is all about removing obstacles to task completion. From that perspective, tablets satisfy a very narrow slice of uses and fail miserably at the rest.
For non-productive tasks, though... I can sit on the couch and look up stuff while watching TV (for those few things I still watch on TV) and the tablet is far more portable for movie-watching, news reading, and light emailing than a laptop, without being as constricting as even the biggest phones are. I don't carry one everywhere but it's definitely one of the things I think of as I'm walking out the door. My kids love tablets (so I regulate their time on them) and being able to video chat with family is a slam dunk.
You don't NEED a tablet but they are useful. They make excellent primary computing devices for people who ONLY have light computing needs. My late 87-year-old grandmother-in-law couldn't use a computer all that well but she rocked on her iPad.