BA started this some years ago, though I mainly see it at European outstations. In LHR T5 I've only very rarely had more than 60 seconds to wait in the jet bridge.
I can see how it allows BA to squeeze extra juice out of its routes, but it can be extremely uncomfortable (European summer jetbridges can be 45 degrees+ at times) feels a pretty hostile thing to make your passengers do. I could have saved £200 and flown Ryanair if I wanted to be exposed to the elements and long queueing.