Your flow is not accurate since you seem to be wanting to follow procedure. Ground crew is wishing well before moving away and before the hand signal is given. Either there is no visual message at the end or there is a voice message before the pushback truck moves away.
You keep missing the point.
It has been said the voice message should be heard, when in fact it shouldn't because, the
GSX pushback guy is already far away from the airplane when the TEXT message says "have a good flight", THAT'S why it correct you won't hear any voice.
Now, you are saying something completely different, that we should change the PROCEDURE to have the guy saying "have a good flight" BEFORE he leaves, that's a completely different issue and yes, IF GSX was made that way, in THAT case it should have the voice too.