problem is indeed lean outside cilinders, with the longest runners. Don't know if BMW did it on the oem cars with 4bbl but US straight six ( Chevy ? ) had different cam lobes between cilinders to compensate that.
This is an interesting problem. I wouldn't say that the outer cylinders get a "lean" mixture, as "lean" implies a lower fuel/air ratio. The carburetor can only deliver one fuel/air ratio, and that will get to all six cylinders. The problem is simply that the outer cylinders get less fuel/air relative to the inner ones, due to friction in the longer chambers and delay = passage length / speed of sound. It would be like the inner cylinders "seeing" a half throttle, while the outer cylinders only "see" a third throttle.
And I suppose that Chevrolet (or whoever) could sort of compensate for this by putting more lift / more duration on the cam lobes for the outer cylinders. So those valves would open wider / longer, letting in more mixture. But both effects - restrictions in the long passages and more mixture with hotter cam profiles - are going to be nonlinear across the RPM range, so getting one to cancel the other would be tough.
Clearly having one choke per cylinder (and equal length exhaust headers) is the ultimate performance solution (like the Offenhauser engine below). But for inexpensive, simple engines intended for street use, a single carb on an inline engine is probably good enough.