I have to agree with Ampharos with this one.
The people who suggest that it isn't broken just clearly don't understand what he is saying.
MONEY IS ON THE LINE.
If I stand to win even $50 dollars from this match, I will do ANYTHING in my power to win. That 50 dollars is a new game for me, a gift for my girlfriend, an extra 50 dollars into my savings and etc.
So now imagine you are playing for $500, even $1000 at a big tourney.
Are you seriously going to tell me that you won't out wait your opponent if that is the best way to insure you get the money?
Let's say one player is MK and the other is playing Marth. Neither have a projectile. Neither can force an approach on the other. If each player stands at the end of Smashville expecting the other to approach it will simply not happen.
If one player approaches that puts them in a lesser position as Brawl favors defense. Therefor it is the best option to simply bore the other player so much into approaching. If you can out wait them and make them come to you, you will have the advantage.
What Ampharos is saying is that who ever has to go to the bathroom first, who ever falls asleep first, who ever has to eat first, or whatever the reason, they will loose. It isn't based on skill anymore. It is based on endurance of that person's body; Smash isn't a test on this. It is about who can take every option given to them to win and use them the most effectively.
Time matches force one character to approach or loose. If I am not forced to approach then why should I? Stalling is part of the game. Smash isn't about having honor or morals when it comes to battle. It is about playing to win. If my best option to win is to take a percent lead and plank and hundreds of dollars is on the line than you better believe I will take that option. I'm winning money, you aren't, who do you think is happier in this situation? It isn't my fault your character can't lob a projectile over the edge of the stage to hit me.
If you aren't going to play to win then don't play. Simple as that.
On the real topic.... Stock matches are tradition and a purely timed match is also deemed uncompetitive. Stamina matches only promote two aspects of the game. Damage and punishing and completely removes the whole landing a kill move factor of the game. It also favors certain characters WAY too much. Fox can just spam B the entire time and use his speed to get out when you get too close to him, Olimar just has to throw Pikmin until you die and etc.