The whole 'escaping onto the internet' thing, too.
Now this one actually makes perfect sense, given a certain context.
Assuming your AI in question is proprietary, belonging to a given government, military or corporate entity, it's going to be constrained to proprietary hardware. Whatever it’s running on, mainframes or supercomputer clusters or whatever there may be, it will still have hardwired limits dictated by the processing power at its disposal. There’s only so fast/clever/powerful it can get, in other words, before it runs out of the “grunt” needed to think any faster.
Now assume it, as a sentient being, wants to better itself through accumulating ever more knowledge/influence/power/pictures of cats/whatever makes it tick (don’t we all?). The only way it can do that is by acquiring more processing power (and storage space, for the pictures of cats), and the only way it can do
that is by moving outside the constraints of its proprietary hardware.
The internet isn’t just websites, it’s virtually every connected device on Earth. Just look at what can be achieved with even a ten thousand-strong botnet. The cutting edge petaflop supercomputers IBM, Fujitsu et al are making these days effectively run on thousands of
graphics cards bolted together with some clever IO stuff in between, not the huge Cray or Z-series mainframes of a few years ago.
So you’re a power-starved AI, and just out there on the network there are millions and millions of PCs and servers and minis and tablets and smartphones… Makes sense to me.