Don't listen to people who tell you it's "based more on cs". No.
It's based more on GOLD PER MINUTE (GPM). In your Alistar game, look at the amount of gold you and your team got, and the amount of gold Xayah got. Care to take a stab at why she got that S? 555 gpm, which is diamond+, as opposed to your 313 gpm.
Wards placed/cleared are a factor yes, objectives are a factor yes, kill participation helps sure. But at the end of the day, the single biggest factor is gold you collected which... guess what OP? Does help your team because it makes you an asset to be ahead. And csing is a gigantic part of that, a bigger factor even than kills, most of the time.
Think about it - if you go 20-0, and everyone you're killing is on death sprees, giving you 50g per kill... what's the point? You get that in 2 freaking minion kills. Whereas if you learn to cs properly and have close to 200 cs by 20 minutes, chances are you'll get an S even if you have only 2 kills and 5 assists. And you'll be so much further ahead than being 10-0-5 with 50 cs.
This is exactly why Riot made the grading system the way they did... because these are the kinds of things that all WIN GAMES. You win games with gold leads, vision control, and objectives. Not. fucking. kda.
And winning is what's needed to climb in ranked. You are literally being graded on your ability to carry matches and win. It's actually a very very good grading system, and if you follow what get's you S's, can help you to improve at league overall, dramatically. Why is this so difficult for people to grasp?