I'm two years late on this answer, but the short answer is because it's basically the only category anyone runs. It would be more accurate to say "no major glitches" than just "Any%", but there aren't really other categories with different glitch-rules for DQ3.

The Japanese community effectively dictates the rules for the SFC runs, because there are about a thousand J runners and about a dozen Western runners. The official name of the category is 通常ED（増殖禁止）, but I don't know any of those kanji or what "ED" stands for. Pretty sure it translates to something like "Beat the game (Bug Limit)". I think the board underneath the main board has different glitch rules but I don't know what the difference is, and there's only one time on that board.

You can see the J boards here: http://niconamarta.sakura.ne.jp/index.php?game=%E3%83%89%E3%83%A9%E3%82%B4%E3%83%B3%E3%82%AF%E3%82%A8%E3%82%B9%E3%83%88%EF%BC%93

I noticed a couple weeks ago that the embedding on all of the JP runs themellin put up is broken. I can still get to the videos through a little element-inspection and url manipulation, but I was told Nico changed how their embed code worked about a year ago and I'm guessing that's what broke these VODs. Is that something we can fix, or is that an SRC thing?

I moderate some of the Dragon Quest SRC boards, and it would be useful if we could give a game multiple names (aliases) so that when you type "Dragon Warrior Monsters 2" into the search bar (the game's English name) it pulls up the board for "Dragon Quest Monsters 2" (the game's Japanese name), where we have a separate category for English runs.

The Dragon Quest series was known as "Dragon Warrior" in the West until whenever DQ8 came out, so a lot of DQ games could benefit from this, and I can think of a couple older series that used to (or still do) have different names in Japan vs the US.