Sure, but if we assume we manage to have a human-level AI, how powerful should we expect it to be if we speed that up by a factor of 10, 100, or more?

As powerful as a a team of 10, 100 human slaves, or a little more, but within the same order or magnitude.

Personally, I'm pretty sure such a think is still powerful enough to take over the world (assuming it is the only such AI), and in any case dangerous enough to lock us all in a future we really don't want.

100 slaves are not going to take over the world.

I'd really like to see someone taboo or at least write out what they mean with this 2-nary purpose. It surely got me confused before, and especially now after the op clarified my thoughts, it feels like a completely meaningless and incoherent utterance.

Can you give any other examples where purpose is used this way in common language with intended 2-nary meaning* except "the ultimate purpose"?

*edited, sorry for the confusing wording

Hypothesis: original (probably Latin) incantations were aliased to "Wingardium Leviosa" and similar because it was easier for Hogwarts students to learn.

Evidence:

• Powerful wizards still use some Latin spells. Perhaps only up to 7h year magic was aliased?
• We did not see any non-English wizards cast spells yet. It's likely (and fits into the setting) there are other syntaxes.
• Due to the Interdict of Merlin, it's possible the Latin alternatives are lost.

The aliasing could be common knowledge among wizards, but not muggleborns. That could explain Hermione not saying anything when Harry snaps at the silliness of it. Still, Draco doesn't mention it when discussing if early wizards were more powerful.

Do readers get to see non-English speakers cast spells in canon?