This research for a concrete historical record of what was the dominant game, stroke or match play is out of my desire to research.
But, if we are looking for social and economic impact, I think they must be separated by common people and skilled elite people to obtain a picture of the early game, prior to say, 1900.
As Michael notes in his set up to the question, the municipal (commoner
) folk just naturally gravitate to matches over ;)a time frame, perhaps creating brackets and a series of matches throughout a field of entries, or it is just pair-ups, catch as catch can, and pairing by 'common' interest, of can so and so beat this other fellow at match play?
Our municipal men's club has two summer series, of match play, one singles and one doubles matches. We are bracketed, and winner moves on. We must schedule our own matches at mutual agreeable times, and have a drop dead date to complete the round. It take 4 rounds of wins to become the champ of the bracket. There are two brackets of skilled players 9 and under handis, and 10 and over, of course played with handicaps. We often have the hot 20 handi beating a good solid 10, which makes it more fun and lots of kibitzing about sandbagging, etc. So, the commeradarie of the smaller than total golfing universe at our muni, (the men's club) have a natural affinity, it eems to me, to enjoy the match play, because it is common.
Medal stroke play for tournaments serves both the higher prize awarding function with awards for wins, places, shows and usually in our fields, swag trade in pro shop down to sometimes 8-10th place if the field flight is strong with 30 or more playing.
And, as the prize money is significant in the pro game, stroke play seems obviously the more preferred method to dole out the booty.
So, on the historical aspect, it seems to me that the commoners, would gravitate to match play, due to a highly socialablilty factor of the game amongst familiar small groups of afficianados that played it, and once a larger field of players, and more prize money was offered, stroke play ascended to dominant status. All conjecture....