POWER. That's why
Although you are right, the Swords of Justice like the Taoist trio are legendary. However, there is a great difference between their power. The average base stat total for a fully evolved Pokemon is around 490, with the Justice league having base stats total of an above average 580, strong but reasonable. The dragons and other version mascots however have ridiculous totals of around 680, with kyurem white and black at a whopping 700. Basically what you end up with is a Pokemon almost twice as strong as the average Pokemon, making the game far too easy. So, the cane limits you to the "lesser" legendaries like the birds, beasts and cows.
*Im on mobile so I'm probably very slow but I hope this helps