Bruce Lee didn't invent that. Maybe they think he did because he introduced a lot of boxing into his version of martial arts. The way he is transfering the weight is wrong- he is punching with the right hand and the weight ends up on the right foot. What are you going to throw next? You certainly aren't coming back with a left hand- look at the position he is in.
You see a lot of mexican fighters throw a similar left hand after slipping a left from an opponent. The thing is, the weight needs to end up on the other foot if you want to throw another punch behind it.
Or maybe it doesn't, because you see a lot of guys working everything off their front foot in this era, but that doesn't make it the optimal way of doing things.