I'm philosophically interested in this kind of relativism. Could we not say that a game that has moves that randomly cause the character to freeze, at random times characters fall through the stage, fighting games with only one playable character, are these not all examples of things that make a game objectively worse? If so it seems like there might be legitimate properties to go by.
As I use the word "competitiveness", let it mean "the margin of difference between the better player's chance of winning a set and the worse player's chance of winning the set."
It is certainly possible to identify specific mechanics that are objectively bad, because they reduce competitiveness. Tripping reduces competitiveness, it's extremely unlikely that the unique skillsets players use to combat tripping (like, I've probably been Pavlovian conditioned to dash 1% less than I would if it didn't exist) overcomes the variance introduced by tripping. It's possible an uncompetitive mechanic could exist because it explores interesting depth or is just fun, for example, the explosive power of pawn promotion in chess probably makes endgames a bit easier to win for weaker players, but pawn promotion strategy is fascinating and most chess players I know, including myself, really like the mechanic. (Chess has luck. Whenever a player can't actually perform the analysis or remember a strategic rule of thumb that supports Move A being better than Move B, they at some point pick Move A arbitrarily and get rewarded or punished. And move A might even be part of an 10 move chain you're looking at .)
Tripping is definitely not one of those mechanics. People don't enjoy it. So there is certainly no particular gain to justify the loss of competitiveness.
In the post you quoted though, I was saying that an entire game should not be considered objectively bad. Smaller aspects of a game can be evaluated, but many are very difficult to evaluate.
Games with an overly dominant character tend to lose competitiveness from that aspect on its own, because the loss of depth leaves less total possible skills for someone to master and get the leg up on someone else, move A vs move B scenarios are more likely to fill the void, or a lucky save from Randall.
Those aren't the only factors though, each game's spacing, mechanics, matchups, and whatever else goes on impacts competitiveness, because there are nuanced ways to get skills at the game to give you the leg up on your opponent. It's very possible for the mechanics of the game to compensate for specific flaws by having good strategy in general, and overall be more competitive.
For an example, when Zendikar came out, I didn't see anything wrong with any of the cards in the set for drafting. From reading high levelled players' feedback though, I found out that the ideal metagame was highly centralized aggro vs. aggro games, and that the simplification made it much harder for strong players to win consistently. Most of them were losing elo rating because it was too close to a coinflip for them to beat a very inferior player, because they both had mastered aggro v aggro drafting and then the shuffles take over. As a layperson I had no idea this was the case. The situation is complex enough that I could be skeptical of those good players' opinion of the format - maybe if they were at an even higher level it becomes a skillfull set - but the changes in stable elos they had had for quite a while demonstrated statistical evidence that competitiveness was getting reduced by hard evidence rather than theory - good players were losing a lot.
When Rise of the Eldrazi came out, I thought the set looked really random. Venerated Teacher was a common card that was either awesome or terrible when you drew him and he added swing to the format, and most of the pro drafters wouldn't disagree on that specific flaw. But even though I could pick out more specific sources of variance like that, I didn't have the big picture - Rise of the Eldrazi has an extremely balanced set of strategies with lots of nuances on playing them well, and in spite of Venerated Teacher it's leagues more competitive than Zendikar. ELOs started returning to normal.
For the competitiveness as a game as a whole, only tournament data can present a good picture on the game's competitiveness. Basketball teams upset eachother all the time but Lance Armstrong or Lenny Krazelberg can win over and over again so I can conclude basketball is a less competitive game than racing sports. But throwing balls into hoops is fun so that's worth it.
To the best of my knowledge, Brawl, Melee, and traditional fighting games have tournament outcomes that reflect a very competitive game. They all are pretty similar in competitiveness, so either tripping is a small fault, or it's a large fault and Brawl has tons of qualities that outweigh it, but either way the tournament data suggests the games are very competitive and it's mostly a matter of which one you like more.
This post is already too long, I will stop now.