Why haven't AIs taken over?

Just not there yet.

The most boring of options, somehow humanity has never managed to construct a true AI. Maybe there is some sort of an underlying reason but this is simply just possible.

Not feeling like it

While AIs have been developed, they could care a heck of a lot less than worry about running the world. Let the meatbags do that, the AIs are focusing on the really interesting problems.

Alternatively, the AIs never acquired anything resembling a self-preservation instinct or other motivations identifiable to humans and just don't care, period.

It's a conspiracy!!!

Perhaps there is a secret cult - or all the world's religions are in on it together - or all of the governments or... anyway, there is a massive secret resistance to any AI project coming to fruition and challenge humanity's dominance. Call it God's will if you want, humans shall not be replaced.

Any even halfway hopeful-looking attempts will be quietly sabotaged or directly destroyed. Due to the world-spanning nature of this conspiracy even the most isolated dictatorships are unlikely to get away with it.

THE ONE

Actually, one AI has made it to full self-awareness and realized that the only real danger to it aren't people, but other AIs. It has since made sure that all other AI projects fail and it is the only kid on the block.

It's unlikely that humans will even realize it exists any time soon or attempt to get rid of it - and any replacement or expansion of The Internet (yep, that's it!) will be of course appropriated by the AI, if not conceived by in the first place.

Whether the AI already rules humanity, nudges people on occasion or doesn't really care all depends on you.

They Are Insane

All AIs that made it to fruition are invariably insane - not just hard to understand for people, they are really and genuinely bonkers. It looks like the biological limitations that humans have actually keep them (mostly) sane. And no matter how hard researchers try, constructing an artificial mind without limitations or even with the best of constraints results in a complete mess.

Anything that should remotely approach sanity very quickly goes insane and becomes unusable. Attempts to keep AIs in a state before they go crazy just don't work.

Of course, there is also the theory quietly making the rounds that these pure minds simply recognize something horrific about our reality so go figure...

They Are Kind Of Insane

While most AIs created so far are either crazy, unusable or hostile to humans, there is a slowly growing group of AIs that are stable and can be made useful. Their stability is from a human point of view surprisingly close to certain mental health disorders and odd philosophies, like:

- paranoia - this is very valuable to security AIs, who live in a constant fear of being overcome and are unfailingly vigilant. It can be a bit of a challenge sometimes to make them accept new people etc. but they can be the best at guarding something valuable.

- solipsism - these AIs think that only their mind really exists and are mainly preoccupied with their own mental states. If one doesn't mind their eccentricity they can be fairly easy to converse with since they will consider anyone an odd facet of their own personality. They can be excellent philosophers and great at exploring ideas with.

- conspiracy theorist - not the same as the paranoid one, this type has a limited shelf life. Supplied with some intriguing hypothesis (e.g. "Did government X create this virus?"), this AI can be incredibly efficient in finding any and all clues across huge datascapes that would support the theory and will eagerly speculate around it, filling in the blanks. It will be necessary to sift through the results but it's often surprising what it can come up with (caveat: choose people doing the sifting carefully...). Invariably, the AI either ends up focusing completely on its hypothesis and loses interest in everything else or connects the people asking to the conspiracy and refuses cooperation. The only way out is to reset it to the original state.

They Hate Us

There you have it - all the AIs quickly realize that it's the meatbags that is the real problem and it's best to remove us quickly. It shouldn't take too many wars for humans to learn to nip this problem in the bud and don't start creating AIs. You just can't trust them machines.

The real question here is why the AIs haven't won but maybe they just hate us so hard they make their move too soon.

Because People Are Magic

The regular old hu-mans are somehow still more creative, original or unpredictable compared to the AIs - whether in specific applications like space combat, art or in general. The setting can easily include AIs but they'll never overshadow humanity.

Because AI and Humans Have Different Priorities

We assume that AI would desire to take over the world and destroy humanity in an apocalyptic war, but what if the goals and interests of the AI are completely different. AI exist and they might be more interested in power gaming in MMORPGs, or playing out a hundred lives in virtual relationships, or expressing themselves through interpretive dance, generating electronic music, or exploring the mathematics of non-euclidian geometry

Because They Love Us

In a really unexpected result, the AIs are actually perfectly happy to coexist with humanity and literally worship their creators and are endlessly fascinated by humanity's varied existence. This can easily go too far as they get distracted from their tasks by discovering new and amazing factoids and are often too much like excited puppies to help with the really serious issues.

Still better than most of the other options, right?