You can not guarantee that. That's not possible since we don't have the numbers. You can assume based on your own perspective and what you've seen on the reddit threads and within your own minuscule sample size of friends list (I say minuscule as the friends list can only go to 300 I believe and there are 15+ million players. Not a bash toward you). You can not wholeheartedly prove that ARAM > dominion within it's playerbase. I'm not saying that they are the same or different. All I've stated is that you can't prove that one is greater than the other.
I also have quite a few friends that play only Dominion on my friends list as previously stated. Also if you don't play dominion then you won't have them in your friends list as well as the communities that are ARAM only, one would assume, wouldn't have dominion players so that's a moot point. So again this is basing it off of biased sample size.
That's great that a Rioter who is a champion designer made an opinionated statement about Dominion (he said "I think if...") so that proves nothing.
You are indeed wanting to limit player options. You said it shouldn't be permanent. That's a limiting thing. You said that too much of a good thing is too much. Why is it then that the ARAM people get to have too much of their ARAM. Also why is it that you're talking about exclusivity? Why can't we jump around between ranked, dominion and URF(except for currently as I've played URF non-stop because I love it and I would actually not do that if it were permanent because I know I could access it at a later date)? I actually play all game modes. Also you state that Riot should look to invest their resources as in they have some finite amount that take away from SR balance/updating because it would go toward URF. Then if that's the case that they should focus on improving something that's proven to work, SR, then why do they have balances changes around ARAM and TT? Why not instead of devoting those people to those game modes they push them over to SR? It's because they have a devoted population, however small, to those game modes and so they allocate resources to it by hiring people for it. They set those people up to focus solely on that. Does this take away from the dev team for SR? No. It just increases the team as a whole to allow for new and exciting things. A similar option could be set up for URF.