Restricting loot rolls not only makes a lot of people annoyed it actually doesn't solve the problem in the first place! People will be annoyed because they may be looking for certain mods, or a certain look, or gear for companions, or crafting materials, or they like the name/icon of the item or any other reason under the sun. To me any of those reasons are valid to need on an item. I am not saying that they are more important than gearing up but the option should exist for having a reasonable shot at the item. As for solving problems this proposal simply doesn't stand up. Consider a dread guard geared marauder rolling need on a medium armor strength columi item. Oops the system just failed at it's goal. Ok so now we include an item level check. But of course we have all seen where the next tiers itemization makes it worse than the current tier. So now the poor marauder is stuck with a higher item level crappy gear and can't roll on a better one. It would also be impossible to "side-grade" for a different itemization.
I have to disagree, "Liking the name or look of a piece of gear" does not qualify for needing when someone in the group has a spec that can use it and it is an upgrade for them. The option DOES exist for having a resonable shot at gear if those are your goals, group with friends or start a group with the intention of getting said gear, rather than joining a group and needing on something for purely superficial or roleplay reasons when a group member can actually use it and benefit from it.
As for creating more loot roll options, well this quickly turns into a mess. Is main-toon off-spec higher priority than third-alt main-spec? What about second-alt off-spec vs. main-toon companion. Yuck! Keep me out of that mess.
I think you're taking the priority roll suggestion way too far, I don't know of any game that takes it to the levels you're suggesting here, the system looks at your current class/specialization and allows you to roll need if the gear matches it, solves a lot of the current issues and if nobody needs it everyone can just greed on it, simple and efficient.