The biggest factor is simply tournament size to get more teams in the tournament and guarantee minimum number of games (in other words maximize potential profits) a time limit is the only way to go. If you limit the teams and follow strictly double elimination you could having games based on innings. I think in a perfect world most of us would prefer a complete seven inning game but especially at rec level that would be almost impossible.
I can talk softball all day
Premier Girls Fastpitch qualifiers are all seven inning, double elimination tourneys(run rules were in place). If you get in the losers bracket you can play 5 games in a row same day. We did that a couple weeks ago, one game was 9 innings 2 hrs 35 minutes and that was 4th game in the day. In tournaments I prefer time limits, for single game in a day like in college or high school go with 7 innings with run rules.