Yup I'm firmly in the battlemap-loving camp here as well, but we still tend to eyeball cover/concealment/line-of-sight, only resorting to tracing corners when someone's life is on the line.
The tactical minigame was a major part of what I loved about 3E, and is an even bigger part of what I love about 4E. We mix as much description and narrative into our combat as we can but there's no doubt that the focus around the battlemap is strategy, tactics, maneuvers, and victory. An exciting encounter area with lots of dynamism and hazards only multiplies the fun.
I agree with KM. But of the two options listed above, I'm for the hard-and-fast rule that speeds up play.Mearls presents something of a false dichotomy.
I prefer a hard and fast rule used by the DM to a vague rule or a grid rule.
The example he gives -- cover -- is better in 3.5/4e than it was in 3.0. But this has little to do with minis (the whole "imaginary lines" stuff is complicated and dumb). It has everything to do with the fact that it only comes in two flavors: cover and superior cover.
Those two flavors are good flavors, and their use is independent of "imaginary lines that cross a barrier blah blah."
The DM can still determine if the creature has cover. Or there can be a rule that says something like "gaining cover in this battle takes a move action." We don't need imaginary lines for cover rules, and we don't need to rely entirely on DM judgement calls and mother-may-I gameplay, either.