That would require a high degree of integration into human society though, which makes it seem very unlikely that AIs would doggedly pursue a common goal that is completely unaligned with human societies.

Extinction or submission of human society via that route could only work if there was a species of AI that would agree to execute a secret plan to overcome the rule of humanity. That seems extremely implausible to me.

How would many different AIs, initially under the control of many different organisations and people, agree on anything? How would some of them secretly infiltrate and leverage human power structures without facing opposition from other equally capable AIs, possibly controlled by humans?

I think it's more plausible to assume a huge diversity of AIs, well integrated into human societies, playing a role in combined human-AI power struggles rather than a species v species scenario.