I'm not here to flame anyone for their build, I would just like to know why still happens.
Some people not only buy it, but also rush it as a 1st item. This is not patch 5.5, when Ludens was introduced and was absolutely broken. We are in patch 5.15 now, after nerfs to its ap, charge generation rate and the passive's ap scaling. There is no real reason to get it as Ahri anymore. As a first item, morello is far more cost efficient and for 3000g you can grab morello+tome (=100ap of ludens) and still have 300g left and a bonus 20% cdr.
Grabbing morello+dcap will make your burst much higher than if you had morello+ludens. Of course an ability with ludens proc outdamages an ability with dcap but even then it's only like 20 damage more and any combo with 2+ abilities does much more damage if you have dcap instead.
If you want a combination of movespeed+damage, lich bane completely outclasses ludens. Not only it procs more often, but a lich bane auto outdamages a ludens proc and it also works on turrets. For the same price.