Kreepy Krawly's answer is nice but I'd like to add some points to it.
Yveltal is the most used Pokemon in SS Ubers and an essential part of the metagame. It is by far the most reliable check to Calyrex-S, with Calyrex-S having to rely on Trick, status, and passive damage to defeat it. It is the most common Defogger in a metagame sorely lacking them, and Yveltal's Knock Off limits switch-ins to the point that most teams have a dedicated Knock Off switch-in just for it. Utility options such as U-turn and Taunt give fantastic momentum, and Yveltal has useful revenge-killing options in Choice Scarf sets, Sucker Punch, and Foul Play. Additionally, the right team support frees Yveltal up to use one of its devastating offensive sets; boosted by Hone Claws or Choice Band in addition to Dark Aura, Knock Off becomes a terrifying move to switch into. Overall, nearly every serious team should strongly consider having Yveltal.
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Yveltal is huge because Calyrex-Shadow is huge. Calyrex-Shadow is one of the best offensive Pokémon in Ubers which can easily clean late-game if your Yveltal, which is its only viable enough check on usual bulky balances, is weakened, and even Calyrex has tricks up its sleeve to weaken Yveltal eventually, thus making overthrowing it easier. So, having a healthy Yveltal is extremely important vs. a Calyrex matchup, otherwise even if you have a better overall matchup, Calyrex can ruin all the fun.
If you check out the Ubers usage statistics for Jan 2022, Yveltal sits at #1 with a whooping 85.2% usage, which is exactly what the above block of text conveys: almost every serious team should incorporate Yveltal in one way or the other.
But checking Calyrex-Shadow is not Yveltal's only reason for clocking >80% usage consistently. It's one of the most versatile Pokémon in Ubers. Offensive Yveltal is one of the most threatening wallbreakers in the tier. Black Glasses, Life Orb, Choice Band and even the extremely niche Choice Specs are threatening offensive sets which can chunk huge holes in any type of build, thus paving way for Pokémon such as Xerneas to sweep. Over here I'd like to point out Hone Claws and Choice Band, which are Yveltal's most fearsome offensive sets as you can claim the 2HKO on Eternatus, its most common switch-in, with a Band-boosted Knock Off, and Knock Off as a whole is an extremely spammable move as removing items from the opposing team is huge, especially against Pokémon such as Ho-Oh. Knock Off + Dual Wingbeat provide unresisted coverage outside some niche Pokémon, so you can click either and expect huge damage to come off. Hone Claws makes Knock Off even more devastating, as a +1 Knock Off has a 93.8% chance to OHKO the usual specially defensive Eternatus sets, and Sucker Punch as a whole is the strongest priority in the metagame, revenge killing Pokémon such as Calyrex-Shadow, Marshadow, Kyogre, Groudon etc.
Recently, fast support Yveltal has been gaining heat too. Fast Utility Yveltal forgoes some defence to run max Speed, thus enabling it to break the usual balance cores with Taunt + Knock Off, while also having enough special defence to switch into Calyrex-Shadow multiple times in a battle. This set is also notable for getting a relatively fast Defog off, which is pretty useful against Sticky Webs teams which are usually dependent on the Speed drop from Webs (and the chip from Stealth Rocks) to get immediate KO's after outspeeding the opponent. Taunt + Toxic Yveltal is a classic combination which was common in the USUM era too, and is known for ripping apart Balance builds and stalls with a Pokémon which can take care of Eternatus, usually Ho-Oh and/or Calyrex-Shadow.
The last set which is commonly seen on Yveltal is Choice Scarf. Choice Scarf Yveltal makes for a decent revenge killer which also provides some powerful utility, especially against offensive builds. Again, vs. Sticky Webs teams, you're usually guaranteed to get your Defog out as you're faster than the whole unboosted meta (outside the niche Regieleki), thus easing the pressure on your team. Choice Scarf Yveltal can also revenge kill Pokémon such as Zekrom, Groudon, Zygarde-Complete, Eternatus, Marshadow, Necrozma-DM etc., which are premier threats in Ubers. As Yveltal forces a lot of switches, you can also viably run Roost on this set to heal off your damage, and Defog is great as a whole on this because of the reasons already stated above.
Overall, it's not only checking Calyrex-Shadow which makes Yveltal the most-used Pokémon in Ubers -- its versatility speaks for itself. You're usually going to see Yveltal on almost every team, and prepping for it and with it is extremely important. This is one of the reasons why I don't like Ubers much, Yveltal is too dominant and over-centralising, in my opinion.
