This is one for the rules committee. Decide what the club wants to do.
I play at a semi-private club with a lot of skilled and dedicated golfers, but the mantra at our place is "play ready golf".
IF you get into regional match-play tournaments, you need the rules committee to explain what to do. How much leeway does the rules committee have in adjusting match-play procedures to encourage ready golf?
This is the way it is.
In match play it can make a difference in the mental aspect of the game. If Player A should hit a very good or a very bad shot, it can affect the strategy used by Player B for his next shot, and maybe even for the remainder of that hole. So order of play can be crucial in match play. With stroke play, you are playing against the entire field, and it isn't necessarily significant what happens in your own group.