Indeed, 'there was no rush'.
During my first go-around, years ago as a very green FO, my training Captain calmly told me our speed was a little high and was I ready for a go-around. I said yes and we performed the manoeuvre calmly. More recently, now as a Captain myself, upon receiving an unexpected out of limits wind report I asked my FO an identical question and the outcome was the same. Taking a breath makes all the difference, but I accept that it's not always possible to do so.
Most jet aircraft can be a handle once the TOGA is pressed and we do not practice 2 engine go-arounds enough in the sim due to time constraints, but essentially it is not a complicated manoeuvre especially if the non-flying pilot is proactive. Similar to a normal departure?
But if you both get behind the aeroplane it is very tricky to recover. And this crew never got the chance to take a deep breath and re-mount their runaway steed. IT never rains, it pours!