I'm gonna highlight this right here:
"1v1s showcase skill over another player and not who's team is snowballing"
This is the exact reason why Riot doesn't make a 1v1 mode. That exact phrasing that says "hey kid, I'm better than you, and the only reason you'll ever beat me is cause I have a bad team and you got carried." It's pretty much that the mode itself is inherently toxic. Don't take my word for it, there's actual evidence of this...it's buried a few YEARS back in these forums, but it's actually right on this site, if the forums have kept record that long.
They had 1v1 and 2v2 on the howling abyss for about a month or so, close to when the map first came out. They at first looked to keep it as an LTO mode, but really haven't used it since. A lot of the players at the time those modes were live pointed out similar concerns to what I just did concerning toxicity, and for good reason. Almost half the population of both of those modes, and a large percentage of the games played, were pretty toxic in the chat logs, and were often held as grudge matches when someone decided it was their teammate's fault they lost the SR game they were all in before they started their 1v1 or 2v2 match. Even in cases where the games weren't a grudge match, there was a high level of personal toxicity through most of the people playing in those modes, especially the 1v1s.
Bottom line is: Toxic players are toxic. Doesn't really matter if its TT, SR, ARAM, 1v1, toxic players are going to find a way to make sure you understand that they're about to have an aneurism from their sodium levels, and that they're blaming everything else for it...especially you.
But in 1v1/2v2 gamemodes, that toxicity feels very much more personal, and riot simply doesn't care to insert a mode that will cause such a huge rise in chat and gameplay bans.