No, Smartwatches Aren't Going To Displace Smartphones -- Or Anything Else
The simplest reason? Ergonomics.
Consider the humble wristwatch. It must fit the wrist snugly, or risk catching and tearing the band on a pocket, door handle, or other object. It cannot be too heavy or generate much heat. One of the major advantages of a wristwatch over a smartwatch is that modern designs typically use batteries that are often kept charged by the motion of the wearer's arm and wrist. The wristwatch is essentially a passive device designed for one function -- telling time. It's explicitly required not to require interaction from the end user.
Smartwatches, in contrast, do require interaction in order to be "smart." They draw far more battery power than a simple ticking timepiece, which means they need to be charged on a regular basis. Unlike a smartphone, which can be charged via wall socket or USB while the user is sitting at a desk, there's not going to be a simple way to charge a watch while wearing it. Limits to screen size require that interactions be driven by single finger or awkward multitouch, but there's virtually no way to read data on a smartwatch while simultaneously swiping -- your finger is too large relative to the size of the screen. Curved screens simply necessitate more awkward wrist positions, larger screens will make the device larger and more awkward.
Taken to it's logical extreme, we all end up with Pipboys. Awesome as that might be, they're not exactly ergonomic.
Functional Pipboy 3000 built by Zacariah Perry
The Dubious Improvement
When Apple debuted the iPhone, it also debuted a much larger screen than was standard for cell phones of the time. That's significant. Not only did smartphones pack better hardware, they offered a new control mechanism and a screen design that could diplay far more information. Part of the allure of a smartphone was that it could do things that were previously confined to dedicated devices (GPS, PDAs) or laptop computers along with a new touch interface that allowed for more intuitive interaction with the device.
What's the allure of a smartwatch? "20% of what your smart phone can do, but worse." This is where physics kills the party. With battery technology improving at about 5% a year and huge thermal limits imposed on any device in direct contact with your skin, the performance curve for smartwatches is going to be sharply curtailed. If you have a smartphone but no laptop, you can replicate many basic computer functions. If you have a smartwatch with no smartphone, you have a device for telling time.
You can't integrate WiFi or cellular connectivity without further hurting performance. Yes, in the long run, that will likely change, but it won't change for any model of smartphone you can buy today. Furthermore, the scale of the problem smartwatches solve amounts to: "I get tired of pulling a phone out of my pocket." Shrinking the smartphone down to watch size might be a positive if it changed nothing about the capability of the final product, but physics doesn't work that way. Screens are smaller, less data can be displayed, typing is effectively impossible, sound is going to be minimal, and battery life for any multimedia functions is going to be a major concern.
Is there a market? Sure, a small one. But a smartwatch that requires close tethering to a smartphone isn't a winning proposition, while a smartwatch with a WiFi and 3G radio would have a battery life measured in minutes. There's little mass market value in a device that needs recharging multiple times a day and can't display enough information to be useful.
More than anything, smartwatches remind me of 3D TV. For several years running, the market was full of predictions that 3D television was the "next big thing." Instead, a combination of ergonomic factors (viewing angles, dizziness, expensive glasses) and the cost of content killed the momentum. 3D may survive as a niche' into the indefinite future, but no one is predicting it'll become the dominant trend in entertainment. Smartwatches are little different.