Say you want to layout a 0.8mm pitch (or even finer) BGA, on a fairly average fab. Maybe not 7 mil trace/space, 5 or 6 looks to be about the minimum, at least with round pads. (Or if that's not adequate motivation, just take any finer BGA or CSP and the next step up from its recommended fab. With a nod to capped vias or HDI, where via-in-pad is acceptable.)
Well, what if you shave down the edges of the pads, making them octagonal, or rounded squares? This could afford, maybe another mil or two of clearance, for traces routed between pads. Doing this on the outermost pads could help fanout. Could be used under the BGA as well, when pads are sparsely connected (so there can be some trace routing on the component layer). It wouldn't do so well for clearing vias (when dogbone style connections are used). Possibly the vias could be shaved as well, but not by much before annular rings get quite questionable.
Tim