Reasons I enjoy match play:
1) Each hole is an individual battle - If you go for broke on one hole and put up a big number, it does not end your round
2) It allows the indepth exploration of the course over many rounds. When playing for "score", I tend to play more conservatively and consistently. In a match, if an architect provides several options of the tee, I will likely try the different options in different matches depending on where the game stands at that juncture.
3) Depending on the course, the day, and the conditions, par is an arbitrary number. Match play is "freeing" because it takes par out of the question and becomes a test between two (or four) golfers over the same terrain in the same conditions.
4) I do not see how the flow of the round or game is interrupted? I see the match as a great novel that slowly builds from hole to hole into a crescendo somewhere on the back nine. Usually, a match is a battle that goes to late into the round. If you are a single digit golfer who finishes the front with a few bogeys or doubles, the round can feel like it is lost before you even make the turn. Unless I am going to shoot somewhere in the 70s, I don't really care what I finish with. 81 or 85 - same difference.
5) Match Play, like links golf, provides a dynamic of "thinking" that rarely occurs on a Parkland course or in stroke play. The golfer is not only playing the course, but his opponent as well. There is another dimension to the challenge.
I think the obsession that many golfers have with score, especially in the US, has been detrimental to the game. People will be on their 10th shot and still plugging away instead of picking up which leads to pace of play issues. The obsession with distance and technology has also been driven by score - if we are all using similar equipment, whatever that may be, it is all good for a match.