You mentioned nothing in your original post about needing to shoot low light, so it seems the 200/2 is not necessary for that reason.
You would save so much money by going with the 70-200/f2.8, especially since you don't need that extra stop. With the money you save over the 200/2, you can pick up a few books on composition in photography, and also on composition in painting (where there is much overlap). Basically, a book that will teach you about rules of composition, about using contrasting elements, about using negative space, about using symmetry, etc etc. You don't need to "kill" your background with f2 when you know how to properly compose a photograph. I used to have the same lust after that lens, luckily I never bought it thanks to the wise words spoken by a professional portrait photographer.
I've got a few buddies who either have the 85/1.2, 135/2, or 200/2, and I just think "what are you doing???" They claim those lenses are great for background separation. You know what else is? ANY lens and a knowledge of composition. I saved so much money, and weight, by going with the 70-200 f4, which is also my most expensive lens. You can tell it eats at my friends' hearts that I am taking better photos with gear that is not high end. But as they always say, a great photographer can take a better photo with an iPhone than a shitty photographer with the best SLR.
I urge you, because I used to be in the same position of lust for that amazing-bokeh lens as you, to reconsider. You have the potential to save so much money, which will increase what you can spend on other things. Not having spent thousands upon thousands (or even tens of thousands) on gear has allowed me to travel much more (which in itself is a lot of fun, whether it be traveling locally, nationally, or even internationally), practice photography more, and just enjoy life more.
Think about it this way. You'd be paying thousands more in order to take pictures where less and less stuff is in focus. Yes, I know that it is a fantastically sharp lens , but let's not kid ourselves about to the real reason most people lust after the lens. Super thin DOF/background separation.
I think that it's helpful to remember that these are all tools, the bodies, lenses, lighting, etc. We all choose different tools based on what we are looking for and how we work.
You have chosen the 70-200 4 as your tool of choice, and apparently it does what you want it to. I don't own it, but from what I've heard it's a great lens. It is, however, a very different tool than the 200 2.
I don't currently have the cash for tools like the 200 2 (or even the 70-200 2.8 IS II), but I did have the chance to pick up the 200 2.8 II for a good price used last year and I have been happy having that as a tool in my kit. Would I say it's better than the 200 2? No. It's a different tool. It's much smaller and less expensive and I've gotten some great images out of it. I will never be able to open it up to 2.0 though, and it will never have that same look. It is a lot easier to fit in my pack on a hike though, which is important to me. Maybe that's not important to the OP. Maybe the cost is no issue. For me the cost (and size) of that lens don't justify a place for that tool in my toolbox. If I had the means, I'd love to have one though.
I think it's odd to criticize someone for asking about a particular tool and then telling them they need to learn more about composition. These are separate things. We should all work on out technique. That should be a given.