It has absolutely no effect on gameplay. Your argument is stupid.
No, actually, in this case it's not a fallacy.
http://en.wikipedia.org/wiki/Slippery_slope#Slippery_slope_arguments
Let's get a few things straight here. First off, our current status quo (as well as the one the game has placed in our hands) is "no tripping is not an option". So in order to change this, you have to give good reasons to do so. Unless I'm missing something, these are your arguments:
1. Everyone hates tripping
2. Tripping is random and therefore makes the game less competitive
Those are your reasons for removing tripping. Let's take them down bit by bit.
1. "Everyone hates something" is
not a valid reason to change the ruleset, until the existence of this thing is alienating a massive swath of the playerbase (for example, even if Mario Bros is a completely legitimate stage, I'd still ban it because without a playerbase, there is no competition, and
nobody wants to play a set on Mario Bros). Personal opinion is an incredibly weak argument.
2. So... the game is less competitive with tripping in it. But guess what: randomness is ingrained into Brawl. You apparently ignored the example of G&W's sideB, so how about a slightly more fitting example: Luigi's Green Missile.
When you dash, you expect to run forwards.
When you use Luigi's sideB, you expect to get a small horizontal boost with minor knockback.
If you trip, you can run into a charged smash, or otherwise get punished, hard.
If you misfire, you can miss your target, or end up too high/too far and end up getting gimped.
So, by this logic, we really should remove Luigi's misfire. Or hell, let me reformat this argument to fit G&W's sideB: when you use it, you expect to hit your opponent and knock him off his feet. When you get a 1, you
will get punished on hit. So let's get rid of the 1 as well, and possibly 2.
Dekar, your argument against tripping is bad. Consequently applied, it leads to not just removing tripping, but also several other gameplay elements. But wait, it gets worse! What about all the
other things in Brawl that are anti-competitive? Surely, brawl would be a better competitive game if Ganon was more viable, no? Well, his fair is
supposed to autocancel. It's actually decidedly a game glitch; you can tell just by looking at the code that someone screwed up. So... let's fix it. Suddenly Ganon is more viable and the game is more competitive. Yay! DDD's infinite on DK... We could make it so that DDD can't regrab without dashing first, making DK more viable. More competitive depth! Yay!
Furthermore, what you seem to be forgetting is that
tripping affects game balance! Even though Luigi and ICs are the only characters with an above-average trip chance (Luigi has a doubled chance; ICs are two at once), this doesn't mean that all the others are affected equally by tripping. Compare Peach's playstyle to Fox or Olimar's. See the problem? Peach almost
never dashes. Fox and Olimar run almost everywhere. People have already mentioned how crucial random tripping can be to Kirby vs. Olimar. Removing tripping ****s with game balance in a way that cannot be allowed.
At a certain point, the game stops being Brawl. It becomes something else. Tampering with the game's mechanics is simply not okay. Never mind the logistical hassle (especially on PAL wiis), brawl without tripping is just not the same game, and at that point, where hacks become the standard, why not play a fully hacked, balanced version that is simply a better game? Hell, we have like 3 fully ready ones, with one more coming out gradually, that we could use, one of which even mirrors brawl's basic gameplay to a T! So... Why not just go straight for that if you want to get rid of tripping?