Order of things that ruin a lot of the fun of this feature:
1) Item type restriction for weapons. I'd love to be able to transmog a dagger to look like a fist weapon, or sword. In fact, that's the only thing that would make fist weapons (which I happen to love the look of) worth grabbing.
2) Legendary restriction. I don't have any, but it's something I'd like to pick up at some point. I'd hate to go through the work to get a legendary item and them retire it a tier later simply because the stats aren't as good anymore. I'll never bother grabbing glaives or any other legendary item from old content just to dance around Stormwind with it.
The first one is by far the one that makes the least amount of sense. I get not wanting Warriors to be able to dual wield staves, but not allowing any other class to change things up a little that otherwise have one and only one option in front of them most of the time? Meh.
Just my opinion here -
1. I wouldn't like there being no distinction anymore between weapon types. I rather like finding out the weapon type of some awesome new epic that just dropped. If I'm just going to transmogrify it to look like whatever weapon type I prefer, then the drop need not have a type in the first place. It could just be an epic stick of type "weapon".
2. It seems to me like the incredible effort that I've gone through to obtain a legendary years ago is diminished if I join a raid and find myself standing around with 24 others who obtained that same legendary a few days ago (and put in much less effort doing so). Nowadays, I'm proud to brandish my legendary anywhere that I find myself not fighting endgame enemies. I don't want to trade away how cool that is, and only get in return... a raid where everyone else appears to be wielding the same thing as me.