There are other reasons, too.
Suppose you could set minimum quality on public orders. Okay. Let’s follow through that line of thought.
Everybody would set max quality.
A crafter starts a work order and fails to craft max quality. He fails the roll. What’s he going to do? Probably abandon the order.
Or maybe he’ll just sit on the order, thinking after he gets some skill-ups he can do it. How unfortunate for the person hoping to have their item made.
Since you can only work on 1 craft order at a time, the crafter’s gonna have to do SOMETHING with it to kick it out of the slot in order to work on anything else. Frustrating for the crafter. Potentially frustrating for the customer, too.
Making all of this worse is the RNG that’s built into the system through the Inspiration stat. Minimum quality public orders might work for a static crafting system, but with Dragonflight crafting so heavy on RNG, it just isn’t feasible.