Welp, that’s going to direly reduce my screen real estate devoted to actual Q&A
I have my browser set to use only half of my screen. Most sites work well this way. Stack Exchange has some of the right-hand navigation cut off, but I don’t need it on a regular basis, and I can see enough there to know when I should scroll over to get the rest.
A responsive design means that, instead of less-important material on the right getting cut off, real estate available to Q&A will be shrunk. Add in another section of navigation, now on the left side—where it won’t be cut off by the default scroll position—and the Q&A space seems likely to be quite limited for me. For reference, my <body> tag reads as having 1075 px in Chrome’s devtools right now.
Sure, it will be responsive, no more horizontal scrolling. Sure, most content is going to shrink down to match. But it means that the margins on the thing I actually care about 90% of the time are going to be that much tighter. Not wild about that; I will likely end up user-styling it away as much as possible.
Anyway, clearly no one user is going to sway you at this point; clearly you have the stats about how many users are likely to be affected (I remember seeing them when the ad size changes happened), but I wanted to point out that this isn’t going to be all joy and glitters.
An actual suggestion: collapse the left nav before taking anything away from Q&A
Make the “collapse point” demonstrated in the video identical to the current fixed width of the Q&A section (from the stylesheet, #questions,#answers{clear:both;width:728px}). In the video, the left navbar collapsed only after the Q&A section got to be what seemed much narrower than that, which means the left navbar is stealing real estate from Q&A. Stealing real estate from the Q&A is badwrong! Don’t do that.
...better yet, just make the navigation always collapsed. Or give us a user preference to make it so. Being able to toggle it collapsed or not, as suggested elsewhere, would be nice, but not if I have to do it every time the page loads.