If this button is going to remove your hand from a perfectly natural control, and then isn't going to do the only thing you could possibly intend it to do, why ISN'T that even enunciated?
The GA button is part of the thrust lever assembly, is a just ahead and slightly underneath the highest point of the levers. You don't take your hand off the levers to use it. Old fashioned gits like me hit the switch and follow the levers forwards to make sure the thing has worked. As you press the button, you call "Go around..." to put your colleague in "go around mode" you pitch up and carry on flying. If you are lucky, your well rehearsed go around procedure then takes place as the pilot monitoring looks for go around power, a positive rate and an appropriate airspeed.
The announciation is not important. The thrust, positive climb rate and appropriate airspeed are. At about 400' the lack of go around guidance, lateral and/or vertical will probably be noticed and then alternative steps will be taken to ensure an appropriate flight path. After landing, you call your technical support people and ask about what just happened. Then the learning starts.
You will find that lots of modes and buttons do not work as advertised. Sometimes you get a message or a ping, sometimes you don't. What is important is that you carry a mental model of what you would like to happen before you need it. Then when you are let down you use another method to get what you want. Saying the button didn't work as advertised when alternative means were available but not used is not really acceptable.