Look at the parties in Arizona State Legislature v. Arizona Independent Redistricting Commission. Any state legislature (or perhaps even any state legislator) that wanted to challenge their state's initiative-back election laws could sue. I'm not that well versed in election law, but it's also possible any state citizen could do it as well. In any event, just looking at the plaintiffs in the flurry of 2020 election cases shows how easy it would be to bring a case back to SCOTUS.
Er, I feel like you're actually deflating your own argument here. Note that the aforementioned clause in the US Constitution grants no power to Congress to dictate how states perform their own legislative elections. The scenario you're envisioning first requires a state to pass an alternative voting system via ballot, then for the state legislature elected by that voting system to sue the state itself to overturn it (which is guaranteed to be wildly unpopular among the electorate that just passed the ballot measure), then for the case to make it to SCOTUS, who can only overturn it for federal elections, not for any state elections, and especially not in state elections in states other than the one that challenged it. A state politician has nothing to gain and everything to lose by supporting such a measure.
The context here is Federal elections for President and Congress--Maine's Federal Senate race is also via rank-choice, as mentioned in the second paragraph/sentence of the linked article. To another commenter's argument that switching to ranked-choice voting for those elections would require bipartisan support, you had retorted that
> Maine voters passed [ranked-choice voting] via ballot measure, no partisan politicking required. Likewise, the two states voting on it this year, Alaska and Massachusetts, are also doing so via ballot measure.
My point is that for Federal congressional elections the legal capacity to use voter initiatives to institute different voting rules, bypassing partisan state legislatures and Congress, will likely be extinguished in the coming years. The same is likely true for Presidential elections as the relevant constitutional language is nearly identical: "Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors...."
My comment about Thomas' view (uncited--I could be misremembering the nuances) about who gets to pass laws controlling state legislature elections was merely to suggest how likely he would be to overturn Arizona; his opinion about the Constitution's and SCOTUS' role in dictating/safeguarding a very specific form of representative government extends beyond a simplistic plain text[1] interpretation of the aforementioned constitutional clauses.
[1] I feel like I should point out that no justice, conservative or otherwise, subscribes to a "plain text" philosophy of constitutional interpretation. Conservative justices tend to espouse either a so-called Original Intent philosophy or Scalia's Original Meaning philosophy, where Original Meaning is not the same thing as plain text. And justices of all political persuasions will make a plain text argument when it suits their interpretation. All things being equal (though they rarely are), everybody tends to agree a plain text defense is the best defense.
