If both pilots hear the pushback clearance, why should the CA have to wait on the FO to read it back and brief him on it, before he tells the tug crew? It’s not that complicated, nor is it a high risk event.

There’s a diffference between rushing and working fast. That being said, not everyone can function at the same pace. Apparently some can’t even get off the gate without feeling insulted by their coworkers.

...and yes when you are dealing with ATC, every second does count. If you don’t believe so, go fly multiple legs to busy airports with flow control, and see how well that out works for ya.