Because it adds a layer of strategy. Football is the only sport where a team can not only control the pace of the game but also the length. Teams can hurry up to get more plays in less time, and they can slow it down to give the other team fewer plays. We’ve seen entire schools of football thought built around the implications of a running clock. The running clock makes the game more complex, more interesting, and gives teams more paths to victory. If the NFL didn’t have a running clock Belichick’s “make Peyton sit on the bench” strategy can’t exist. If the NFL didn’t have a running clock Chip Kelly’s blur offense can’t exist.
I'm not even sure how much the running clock really impacts the end result on the field (in terms of giving one team an advantage over another), anyway. I checked this quickly and came across some numbers on this:
1. The Houston Texans averaged 69.9 offensive plays per game this past season, the most in the NFL. The St. Louis Rams averaged the fewest (57.5). Neither team was terribly impressive.
2. The Denver Broncos and Carolina Panthers had the exact same average: 66.2 plays per game.
3. New England averaged 65.7 and Arizona averaged 64.7, for whatever that's worth.
4. For all their offensive plays, Houston only ranked #15 in possession time this season, at 30:29. Atlanta led the NFL at 32:11, while Philly was the worst at 25:51.
5. San Diego and Houston tied for the league lead in "play count differential," averaging 8.81 more offensive plays per game than their opponents. There doesn't seem to be any correlation between this figure and a team's success. Denver was +1.44 and Carolina was +0.13.