As much as this is a good idea, I'm not too sure this would work out well, in terms of the plot. If you were to join the NCR military, you would be promoted really quickly, in terms of merit alone; after all, you are able to wipe out whole armies by yourself, and your intervention alone is enough to not only break stalemates but also obtain total victory for the side you support.
The movement limitation aside (I don't think the NCR is fine with letting their generals walk out into the desert without an escort, etc.), whatever the player does reflects on the NCR, so if he decides to, say, take over the Strip, it would not be some guy coming in and usurping power, it would be the NCR occupying the place. The political ramifications of that, as well as NCR redtape, regulations, policies and laws would severely limit freedom of gameplay and plot.
Of course, if the player chooses to join the NCR, then it would be a self inflicted restriction, but a different story would then have to be written. Therefore, I don't think Bethesda would be too quick to put this into Fallout 4. Assuming it is even coming out anytime soon, of course.
As a side note, with all the talk about Fallout 4 being centered around the Institute, it would be funny to have a faction made up of MIT scientists, students, etc.