If a professional public transport pilot cannot make a 20 second PA while posistioning from a GA he is probably not suitable for command.
Nominee for stupid comment of the week!
Try that at Innsbruck or Salzberg or.....etc.
Most professional pilots have a great deal of interest in what goes on behind them. However the priority is as always to safely fly the aircraft and then communicate a game plan with ATC. Once time permits, a reassuring PA to the passengers can be delivered, which should be far more informative than something rushed or hurried into a constrained time slot.
Many airlines now have a set PA from the cabin crew in the event of a go-around that basically confirms the regularity of the procedure and notifies the passengers that the captain will give further details as time permits.