I have a right-front set-up on a couple bikes... and I really should change over several others too. First of all, it is pretty easy to quickly remember this switch-over on a bike so it's not a problem at all if you're concerned about having to "re-think" how you brake.
Most of my bikes have center-pull or cantilever brakes so this is never a problem, technically speaking.
Yes! Exactly as LucasA just mentioned, I find this orientation is a MAJOR advantage when making fast left turns onto a side street... across on-coming traffic... and while keeping toward the center of the road... and continuing to signal with my left hand/arm - which also clearly alerts any following traffic of my intention so that they need not hesitate to pass me on my right side. This really makes great sense on the single lane suburban streets close to where I live. This is one of the most critical braking situations which I ever encounter. It is great when my right hand can remain modulating the front brake - which is far safer to use during turns than a rear brake and I can continue my hand signals with my left. A sharp 90 degree left turn is definitely NOT something I am happy performing with a rear brake alone. Maybe I'm just odd, but I really have to slow down considerably when I'm required to do this --- anyone else?
I'm actually rather surprised that this is the more common traditional orientation on British bikes because of the right side driving over there, precisely because of the reason stated above.
With my bikes which have side-pull brake calipers, the typical orientation for cable entry on the caliper is on the right side of the stem for the front brakes [this is true of most brake calipers]. With conventional levers (with top-exiting cables) I think this makes the Left-front somewhat more logical "mechanically" at least - since it seems to allow the cable to exit the lever and loop the cable over the stem in a gentler, less constricted, arc. It also allows an aero-lever routed brake cable to follow its line more naturally from the bar and across toward the front caliper... rather than having to curve awkwardly back again after exiting near the center of the handlebar. But, I suppose an aero brake routing for front-right could simply exit the cable from farther out on the handlebar, maybe dropping down from near the corner of the bar. I've never tried this, but it seems like it would make the bar feel cluttered with such an odd cable exit location.
But, what about STI/ERGO controls?
With modern integrated shift/brake levers you are really locked into and limited by the preferred right/left routings designed into the shifter function of the levers. It seems there is no possibility for easily reversing shift operations on these levers. And, since the derailleur functions are designed for Left-Front, it would probably not be at all wise to separate the brake function of the lever. Especially since both the brake and shift functions are actuated without moving the hand from the lever at all, this actually could cause some serious confusion... but, maybe I'm wrong.
--- Has anyone ever switched their brake cables over on modern integrated road lever controls?