Except every single one of each of those champions with the exception of Annie are picked because of their kits as a whole, not one specific thing they do. Veigar was specifically cited as a pro player as being a "stun bot". Annie occupies a similar space, where she's used pretty much entirely for Tibbers stun and the rest of her kit is kind of irrelevant. But at least Annie needs to cast the rest of her abilities to get her stun up. Veigar, as far as the LCS is concerned, basically only has his E. It says a lot about him if he has only one useful ability to professional players but is picked by them anyways.
However, every single one of Ahri's abilities are important to why she's strong. You brought up her least important ability, sure, but Ahri's foxfire is more crucial to her LCS play than Veigar's Q or W was to his. Her passive combined with her good mana costs give her near indefinite laning compared to other mages - remove it, and she would fall off in play. Her Q is the brunt of her upfront burst, forms most of her poke, and gives her good kiting - remove it, she would fall off in play. Her W gives her reliable multi-target damage, but I will concede it is her least important ability and doesn't contribute much to her overall strength. Her E gives her absurd pick potential - remove it, she falls off from play. Her ult gives her absurd kiting, absurd chasing, strong repositioning, and decent damage. Her ult is extremely important to her, whereas LCS stunbot support Veigar doesn't care about his ult nearly as much as he cares about his E.
Orianna's kit as a whole is insanely useful. Unlike Veigar, her power budget is pretty evenly spread among her abilities, whereas 90 percent of Veigar's is contained in his E.
Once again, Xerath's power budget is spread around much better. His passive, Q, W, E, and R are all extremely important to how he's played. His Q forms the brunt of his poke and comprises half of his waveclear patterns - without it, he's useless. His W gives him another good long range damage/waveclear ability, as well as giving him some nice utility. His E is extremely important because it's his only defense mechanism as well as a decent ability for getting picks. His R is good for finishing stragglers as well as just plinking people who are too busy in teamfights to dodge the damage. Once again, compare to LCS stunbot Veigar, who only needs his E to do what he needs to do.
Lissandra is much the same way. Her passive, like Xeraths, contributes to near endless in-lane harass. Her Q comprises the brunt of her waveclear and poke and gives her good utility. Her W is good both offensively and defensively. Her E is her initiate and escape. Her ult is self explantory. Without any of those abilities she would be trash.
You could almost literally have taken Veigars Q or W away and he would still have been played in the LCS. That is not true for any of those champions, even Annie, because she at least needs to charge her stun with spellcasts.
Charm picks off stragglers. Who cares about that rotating foxfire? Or that spellvamp?
Tibbers Initiation. Who cares about the E? Or Tibbers pet?
Ball transfer Ult Actually, all her abilties are pretty useful for any situation.
Poke Artillery Sniper Ult. He's picked for what his kit revolves around.
That utility team fight kit. Suppress the ADC with the click of a button? Or initiate with ult for free Zhonyas?
the new Luden's Echo and his R ratio is almost back to where it was, if not better, but only at certain times rather than it being constantly powerful.
