I've thought about this recently, and the solution is the Oculus Rift or some incarnation of VR. Mounting the monitors is really the only major technical challenge to the setup you describe, and not being able to adjust your distance to mounted monitors would also be a real problem. The current Rift dev kit does not have sufficient resolution to do computer work, and the new units still will not have nearly the pixel density of modern monitors, but what you lose in pixel density you gain in screen real estate.

The rift basically surrounds you in a digital environment, and a few people have already started to show off desktop environments that work in VR. Working at your computer in VR means a few major benefits:

-Your workstation is no longer defined by the physical space it resides in, so it can go with you wherever you want, such as on the train, in your self-driving car, etc.

-Your workspace is no longer limited to several constrained rectangles in front of you - you pay for a single display device and get a workspace that literally surrounds you.

-You are no longer required to sit upright staring forward, something we have generally acknowledged isn't good for you. Some people spend more money on a nice chair than the cost of an Oculus Rift just to save their back. Not needing to stare forward to view monitors means you can work in any orientation, such as a comfortable reclined position. The staple of starship captains and movie hackers, the reclined "dentist" style chair is generally represented in movies as the way people would sit if they had sufficient resources, such as their own hollywood set building team.

-Your workspace is 3D, but not gimmick 3D monitor style - actual immersive 3D, so your applications could take advantage of this for more contextual information and improved workflow.

-You have total privacy - no one can see what you are working on in VR, so no one can look over your shoulder. That is until they make virtual coworking spaces. Which will happen.

-Your workspace can be flying through the cosmos, on a beach in Aruba, on a NASCAR track, or anywhere else you find interesting. You could be immersed in front row seats of a live tennis match while you work on your TPS reports. You could work on new VR applications inside of your new VR applications, for the ultimate inception "yo dawg" moment.

Cons:
We will become like the people in WALLE.

But... will we? I work from home. I have a standard desktop and 3 monitors. I wake up, walk to the kitchen, make breakfast, then walk to the office to work. Google shopping Express delivers my groceries. Amazon delivers most of my other goods. If I had a self driving car I wouldn't even need to participate in my own transportation when it was needed. What does this mean? It means the future is already on it's way to becoming so convenient that a nearly 100% sedentary lifestyle is entirely possible even for first world people who maintain full employment. For people like me, a dentist chair and virtual reality workstation will not make me any more sedentary - I took 300 steps the other day. I can't really hit much lower of a limit on that.

All this means is that I need to take control of my own exercise routine. I need to force myself to work out, as my daily life does not provide sufficient exercise as is. People who do not do this will become fat, like those in WALLE. But being fat is clearly regarded as unhealthy, and our society is becoming aware of the dangers of unchecked obesity. As we get a handle on appropriate health care in the first world, we will need to encourage people to work out.

For now, I ride a bike, but if I had a self driving car that could take me to the gym while I worked on email, perhaps I'd get out and socialize more.

Rant/Aside:
People are pretty dismissive of some of the amazing new tech coming out. Amazon wants to totally eliminate the cost of human labor for delivering goods by using drones, and people just say "but yeah Skynet haha. It's dumb anyway". Virtual reality is actually happening and it's a revolutionary new kind of display device that I know will change the world, and people say "but yeah the virtual boy sucked. this is just more hype, VR will never happen, or it doesn't matter." Robotics in general can change the nature of how we consume things by eliminating all human costs. Robots have fixed costs that can be amortized down to nearly zero for incremental labor, something that is not possible for human workers. We should embrace the technology of the future and figure out how it can be used to do positive things, rather than dismiss it for it's capability to do bad. Skynet jokes are old hat. Lets talk about how much better we can make the future.

Another note: Virtual reality and telepresence can eliminate the "AI problem" for robots - that is, we have been able to make robots that can do neat stuff for a long time, but giving them any intelligence has been a so far intractable problem. A remote human operator could control a robot worker with much more precision than our current AI technology, transporting human intelligence into a robot and eliminating the need for comprehensive AI. VR enables 1:1 viewing of remote 3D environments, something a monitor does not provide. This will lead to both good and bad new technology, but as they say - you take the good with the bad.