Bronze question: Why does Xerath see high-ELO play?

I hear a lot about how the mobility meta makes it hard to play low-mobility champions (e.g. Veigar). I understand those arguments and I think they're sound.

I see Xerath a lot in the LCS though. As best I can tell, he is not very mobile. He has an average (high end of average?) movespeed. His Q slows him and his R roots him. He has no dashes. And so I would like to know how Xerath survives in the mobility meta.

Is it because the mobility meta isn't the dominant force it's made out to be? (I don't think so, because I understand the arguments for why it is OP, but I'm looking at all possibilities I can think of.) Is it because he has high scalings? (I wouldn't know, I play mostly supports and tanks and wouldn't know good scaling if it bit me in the face.) Is it because he has a slow and a stun on his W and his E? ETA: Is it because his ult allows him to snipe while staying out of danger?

And once we've identified what makes Xerath so strong in a mobility-dominated meta, can that knowledge be useful when trying to come up with balance suggestions like we do so often? (E.g. maybe suggesting that Veigar could have better CC, like a slow on Dark Matter's target area before it hits—which could interact really well with the new delay on Event Horizon—instead of being all OMG RITO PLS NURF ZED/LEE/KALISTA/FOTM.)

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EDIT 2: From the comments so far, it seems that range is one of the characteristics that makes Xerath OP enough to play in LCS (and if you're being played in LCS, it's because you're easier to abuse, so yes, Xerath is OP in these players' hands). Interesting. I always hear about CC being the counter to mobility, but is range another counter? Is this a discussion worth having, as a community?

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EDIT 3: Range keeps being the consistent answer. What if Zed/Lee/Kalista/etc range was nerfed? Would this impact the game positively? Would this still let the mobile champs be playable?

Also, why does waveclear come up so consistently? My understanding is it's a liability because you can't farm under tower if you're always pushing, but does it become an advantage when you're teamfighting? (I'm Bronze. I freely admit it. This is the first time I'm trying to understand stuff like this because the LCS makes good weekend watching. Explain it to me like I'm Bronze, not like I'm stupid. *insert joke here*)