Much as I love match play, I doubt it has much to do with the growth of golf.
I'm not sure what the issues that haunt golf today are in the US. However, I love match play, and I don't think playing more competitions or having more people playing in match play would help solve them.
If the big issue is getting more people to play, I don't see how match play overcomes the initial problem of basic competency... i.e. golf is too hard to learn. Does match play change the equation with respect to access or cost?
Even if the average round time suddenly decreased to 3:15 due to match play rules, I don't think this would increase play. In fact, in Scotland, where the average round length is much shorter, I think there are several "issues" with the game not growing...