Interesting comment, although I can't praise you on all of them some of them make good points. However you're looking at this too complexly URF shouldn't be meant to be played as a "meta" game mode or even needed to be balanced, URF itself is the solution. If we saw new champions being played in a number of different ways, followed by Riot making changes, then theoretically there should be a large amount of diversity in playing each champion because no one is technically "the best" in URF, who's "created" the meta where so and so champion is the best champion hands down, no, URF hadn't been long enough on live for someone to even come close to this. There's also gonna be a meta no matter what, you can't control this, without nerfs/buffs/items that is. Like right now you're bound to see at least Ahri, Azir, J4, Gnar in solo queue almost every game either banned or picked. I would even go as far as to say URF promotes anti-meta, for example I myself half way through URF was kinda pissed at all the Zed's and LB's one shotting me while I was squishy, then one game it hit me, Swain, his infinite ult was the solution was for tankiness, sustain, and not getting one shotted so I went to the store and instantly bought him, it did take me a few games to get use to him but when I did it was really fun. I even went to play him fairly successful after URF in solo queue, and how many Urgots, Sonas, Skarners, Alistars, and other non-meta picks at the time did you see on URF, fairly more than usual. All I am saying is that in URF every champion is theoretically given a chance to be able to be played as a really strong pick, and you know why? Because of the PLAYERS, in my opinion League of Legends players are some of the most creative people I've ever seen, with being able to play odd picks at odd roles, and fairly well or even better than currently strong picks at said role.
With all that being said in my opinion Riot needs to only do 2 things in URF and do it good:
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Fix champs where they are OP enough to take down baron at spawn, render you completely paralyzed to the point where you can't take a step without dying, or never die i.e. Sona/Maokai, Teemo, Zilean. I don't know the "best" possible solutions to these but I'm sure Riot can easily come up with them
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Probably the more important one, make an MMR or ELO exclusively for URF where it's based on the number of wins and games played respectfully. This way players with more experience play with each other and if one player discovers a certain champion does something extremely well and practically carries the game single-handedly then he deserves to win for putting the time and effort to discovering things. I feel like this way people who know better/more will at the top and people who don't know who are "the best" picks will play each other and to me that's perfectly understandable.
Sorry for the long post and if I am not clear enough, I am not really good with words and I feel like this isn't exactly what I'm trying to say but it's the gist of it.
EDIT: Since this was kinda long (from KILLER X 12) I did not bother to proof read this, and i do not intend to. lol Peace.