I'm not saying Dominion needs to stay, but..
Dominion offers something unique among all the modes currently in LoL, and that's the ability to spitball builds and new champions in an environment with lots of built in mechanics to keep every player at around the same power level. Every time a new champion released, I would immediately take them to dominion. It's nothing but teamfights, and dying once or twice wouldn't immediately condemn your team to 40+ minutes of suffering like it could on SR. Even if I would do poorly, I still always felt that I was getting tangible experience with the champion's mechanics, and how they worked as a part of a team.
I know a couple people will cite co-op and/or normal queues as the proper places to practice, but bot games offer absolutely nothing when you're trying to test a champion or build against other players, and practicing or trying off-the-wall builds in in normals are good ways to make four other people absolutely hate you in ten minutes or less. ARAM is also completely off the table, since by its very definition you can't choose a champion to play. Treeline? It's arguably even more snowball prone than SR is at this point due to the small size of the map, and the fact that one person getting ahead is a third of the team being strong as opposed to a fifth. There's still no room for error.
I personally couldn't care less about the map "not looking like it's up to the quality standard" of SR. That's not the reason I play it. It's been made painfully clear to me that the mode will never have a competitive side, and I'm absolutely okay with that, but I'm not okay with having the best training ground for new champions or build ideas get chucked out the window. As a mode, I admittedly didn't think it was very fun, and I agree that it didn't end up meshing very well with the MOBA playstyle.
As far as finding a better solution, I don't really have a lot of ideas (SMITE's arena mode springs to mind as a similar case), but I can throw out what I believe are the core reasons Dominion became my absolute go-to testing ground in LoL.
Firstly, the fact that there were a ton of "rubber band" mechanics that made sure there was never TOO much of a power differential between champions. Of course kills still mattered, and would give you tangible benefits, but they didn't absolutely cripple the opposition to the extent that they do in SR. Missing out on minion gold and XP wasn't a factor, and neither was losing map pressure by losing your turret ten minutes into the game.
Secondly, games of Dominion were never won or lost based on one member of your team being picked off for being out of position. You either played to the objective or you didn't. In SR, at least at my elo, it seems very common that giving up one kill for a stupid reason can easily snowball you into a terrible position by allowing the other team free roam of the map. In dominion, this wasn't the case. Revive trinket was a thing, and if you danced around the point properly, nearly any champion could hold the line for a very long time.
Thirdly, the games were much faster paced than SR games, usually clocking in under 30 minutes, where SR games have historically been 30 minutes at minimum, and ranging from there up to 75+ minutes long.
tl;dr: not trying to campaign for keeping dominion alive, but League is losing a great low-stress environment for testing new champions and strategies against human opponents, and not the goldfish that operate intermediate bots.