If someone is going to defend it, defend it right. I played competitive Brawl for many years, going to around 50 tournaments from locals to nationals. Random tripping happens to you 0-3 times a match, with 1 or 2 being the normal. When you randomly trip, there are tons of invincibility frames associated with each roll, only leaving you vulnerable near the end. This can help, hinder, or do nothing for you. I'll start with the most common:
Nothing: Random tripping in a competitive environment generally does nothing. Why? It's important to know the competitive defensive play of Brawl. When you approach in competitive Brawl, the general reaction is to shield attacks in order to punish or run away. There is almost never an advantage to try and be offensive when someone is running towards you. Thus, if you approach and trip, chances are you won't be phased. You'll trip, instantly press a direction, and get up unscathed because you shouldn't have been near them in the first place. There's no reason to dash if you're close in Brawl, as running through someone has no benefits and is easily punished, walking is a much better option as smash attacks can be used out of it. The only way this turns in to a problem is if you do something expected with your roll (Rolling away from the opponent is grounds for being tech chased) or you don't get straight up. The number of frames to get punished by holding up after randomly tripping is extremely small, I can't even think of a time I was hit during it. You can also use a get-up attack out of tripping, but it's not very useful as it has much fewer invincibility frames and is typically unsafe on shield.
Helps: The next common. How can tripping help you? Again, the invincibility frames. Trying to run away from Snake's weapons? You may trip through them and go unscathed, especially with a well timed get-up. Trying to get away from an opponent that is up close? You may trip through their surprise attack/grab and roll away. Almost never will you be hit out of a trip during competitive play. When it happens, the attacking player never has chance to react to it because it's absolutely unexpected. Random tripping helps out far more times than when it...
Hinders: The rarest. I can't remember a single time in all of my tournaments and practice for years where I've been totally hindered by a trip. There may be times where I took a random laser for 2% or got tech chased and took maybe 15%, but they were few and it never lead to death. Beyond a few cases in tournament play where it has lead to death (Always by the attackers accident), it has almost never caused problems in any of the hundreds of Brawl matches I watched. The window to punish is too small and your options to get out of it are typically fast enough or safe enough to be perfectly fine in the overly-defensive play of competitive Brawl.
So if random tripping helps more than it hinders, and does nothing far more than it helps, this leaves us with what? Random tripping is really not that bad. It's silly and fun to joke about mid-match, it can make you frustrated that you lost whatever setup you were trying to do, but it never really makes or breaks anything. The only reason it doesn't belong in Smash is because it is a randomized function that takes away control from the player for a second, which is fundamentally flawed. Other than that, it's not so bad.
tl;dr Tripping generally does nothing and helps far more than it hinders due to the defensive play of competitive Brawl.