I like the general idea of making the game more accessible to people with different patience levels. I do feel that your idea could be tweaked a bit so that it's not a variation on something we already have, though. The ability to choose how long your pet is hoarding would be pretty cool, even if it's just two or three options. Scaling the rarity of loot based on time, as much as it makes sense, I have to disagree with for the same reasons as Icearashi (whose posts could have been worded more constructively...). Rarity excluder potions are sort of the Pandora's Box of this game; we can't really get rid of them now that we have them (long story), and they're important to the economy. But maybe being able to choose a longer hoard time could guarantee that your pet brings back a certain amount of items, or choosing a really short hoard time might only guarantee exp and/or PC. Or, to get closer to your original idea, the loot rarity would scale with the hoard time, but only slightly, so that this is much less potent than a rarity excluder potion. For example, even the longest hoard time might only guarantee loot rarity at 60% and below.

I know it's not what you had in mind, but those are the only things I can think of that would prevent a clash with rarity excluders. As I said I do like the overall idea of "quicker" ways to play the game for people who don't have as much patience. As Icearashi said, hoard times have already been shortened more than once, but it's clear that we're going to keep getting suggestions to shorten it until there's a solution for those who want to come back to the site more often.