Artifact Power is not gaining stacks in the way described.

[Sheepofthenight]

On every class I have seen, you can watch you character cast skills and it won't always increase the Artifact power stack. This is happening even without multi casting, just watching the basic cooldown tick doesn't always increase the stack. If it's just a chance to get a stack that should be communicated in the wording.

[Game Smithing]

Hey Sheepofthenight! Regardless of which weapon or character you have, it is always a chance to gain artifact power per cast. This chance is also normalized by the base cooldown of the skill being used, so it should be fairly similar if you have a build with a lot of fast skills or a lot of slower skills. This is reflected in-game, in the power up you have that actually does the job of granting you artifact power (screenshot below):

https://ibb.co/KVK1mKd

This is not the most obvious place to check for this tooltip, but this information would make the "more details" of the artifact power skills too long (it is already longer than we would like).

[Sheepofthenight]

Ah okay, thanks for the answer!