YES!
It did solve a real problem, it just did so badly - it was heavy, expensive, clunky, and had no suspension so could not handle much surface imperfection.
I think Kamen's big mistake was that he was pathologically afraid of anything smacking of speed, competition, or plain fun. He explicitly worked to avoid any association or possible diversion of use of the Segway in anything like that, because he thought a key audience was city planners who hated skateboards, and thus any fun at all would result in them being banned from city use. Maybe he's right, but if so, the solution space was zero.
Yet, that total avoidance of fun resulted in a number of disasterous results. First, as PG pointed out, the users all looked like dorks - because they were riding a device designed only for dorks.
This also resulted in zero engineering being dedicated to performance, and the, IMO, insane decision to have no suspension. This resulted in the spectacle of President Bush falling off one on his very public ride, simply from riding over a very small hole. Another very public black eye.
and the general absolutely clunky engineering of the thing resulted in no fun, no enthusiasm, and the only real use case being the mall cop market. And a few isolated groups playing Segway Polo is not exactly an activity to generate enthusiasm.
I'm quite convinced that if he'd engineered the thing to be fun, or at least hackable to be fun, it would have taken off. It would have been much more streamlined, cool looking higher performance, and with a suspension to be able to handle at least a bit of terrain (heck even 2" of travel would have made a huge difference). It would not have been that hard to add a "Calm Zone Mode" akin to phone's Airplane Mode for use in the city...
But, that's all history now