For me the biggest pro of a loser’s bracket is that a weaker competitor is going to be able to get double the experience. Even if they lose every match, it’s such a valuable learning experience that helps them become stronger next time and builds the sport as a whole. Getting blown out and going home immediately leaves a lot less opportunity for growth.
The con is that loser’s brackets actually make underdog/upset victories less likely. With single elimination, one bad matchup or unlucky moment can eliminate a high seed permanently. While a loser’s bracket gives weak teams more experience, it doesn’t do much to increase their chances of winning the whole thing. For strong teams, a loser’s bracket allows them to make a mistake and stay in the game. It’s also arguable it gives strong teams an easier path to victory. Losing right away, beating a bunch of weak teams, and advancing to the grand finals against weaker competition is a viable, if risky, play.
Non-bracket formats solve a lot of these problems, but have their own issues. The bracket is still probably the most entertaining for spectators.