Unique Character Teams do not prevent tier whoring because all the tier whores are still going to play, just in different teams. Now with a Ciel on every single team, we're much more likely to see every single Ciel play...the exact same way...with plenty of Ciel vs Ciel matches (BORING!). Now consider if Duplicate Character Teams were allowed. Now, all the tier whores would be teamed together. Now we're much LESS likely to see Ciel mirrors as well as not having to see some play at all.
If there's a ciel/random/random team vs ciel/random/random team vs a ciel/random/random team, we might see a Ciel vs Ciel matches that might be boring, but we see only few of it. If it's ciel/ciel/ciel team vs random/random/random team, we see ciel at least three times in one tournament round. To me at least, few mirror match is much better than sitting through watching a round where the entire team is just ciel again and again regardless of whether they win or lose.
Percentage wise, ciels (I'm just using ciel for no reason) spread out in teams would create small chance of mirror matches as it's 3 on 3, while 3 ciels on a team would mean 100% matches of that team being consecutively ciel. I have no problem seeing any one character play. As with any fighting games, it's just boring if one has to see it repeatedly.
If this rule somehow discourages people who would have entered to not enter, then I'm all for not using this rule. However, I do not see how such a common rule inconveniences people to such an extent that they will not play at all. If you were gunning for the title with every possible tool that can be used that might have an effect, but if you were entering to have fun playing competitive matches while trying for the title, teaming up with someone else would not be such a problem.
In fact, there are tournaments called random tournaments. They're where people just show up and get randomly assigned a teammate to play with. It probably can't be used in the Melty Cup because of it's seriousness (cost & reputation), but it's a fun type of a tournament where the focus really just becomes having fun playing competitive matches.