You're making a subjective judgment here on the quality of these critics though. I mean it's Rolling Stone, the biggest music magazine of all time. These lists come out roughly once a decade, so a lot of consideration is going into them.
Just because you disagree with the ranking doesn't mean that they don't know their stuff or weren't rigorous about it. If you really don't like this list, show me a better one, and I'll show you a list whose editors just happen to agree with your tastes more than the editors of the Rolling Stone list does.
Rolling Stone has significantly larger worldwide circulation than all of those magazines (in some cases by an order of magnitude or more). In addition, some of the magazines you listed no longer exist, whereas Rolling Stone still does. E.g. NME ended its print publication in 2018 and Melody Maker ceased entirely in 2000.
You got any other examples of magazines you think are bigger/more relevant than Rolling Stone? Because none of these fit the bill.
>Rolling Stone has significantly larger worldwide circulation than all of those magazines (in some cases by an order of magnitude or more). In addition, some of the magazines you listed no longer exist, whereas Rolling Stone still does.
The RS is just something read by aging boomers. It hasn't been relevant since the 70s. And even then, after an initial period, it was for the politics/culture/gossip content, not the music.
The circulation is not really relevant. If you follow the music world, press, interviews, behind the scenes, biographies, etc., RS has never been influencial for actual musicians/execs/fans/etc. The other magazines mentioned, have.
NME, Melody Maker were far more relevant in the 1980-1995 period (yeah, that's UK, but UK had an unproportionate influence in US music as well. Not just in punk, post punk, new wave, and electronic music, which it close to dominated, but back to the Beatles, Stones, Led Zeppelin, Black Sabbath, Who, and so on (all British).
As for something actually influential for post-2000, that would be something like Pitchfork.
Just because you disagree with the ranking doesn't mean that they don't know their stuff or weren't rigorous about it. If you really don't like this list, show me a better one, and I'll show you a list whose editors just happen to agree with your tastes more than the editors of the Rolling Stone list does.