I'm not so sure about that. I don't doubt they have the skill to do it, but I doubt they can make the numbers work. Apple can make custom CPU cores because they sell a shitload of phones. Google does not.

Maybe they would license it to manufacturers - use our core design AND our operating system gratis, as long as you send users to our services?

Googles ad revenue is so important that they should do absolutely anything and everything to protect it, spending billions on R&D to keep android at the forefront is essential, and at the moment they are only really competitive on the software side (A11 smokes latest snapdragon chips, as does the A10....), offering a custom chip would give android the vertical integration that Apple leverage to be so dominant.

It also gives leverage over Qualcomm etc. wrt availability of security updates.

I'm not so sure... Have they bought or hired any taken like apple did?

You're begging the question here. Apple's acquisition of PA Semi filled a void. You assume a similar void.

The sophistication of the team you need to plug together components into a workable SoC or design something like the TPU processor core is much less than what you'd need to design a top of the line OoO application core. They clearly do have a team that can put together SoCs like the original TPU and if they keep working at it I'm sure they'll be able to train up to doing that eventually but I'd expect a decade long learning process unless they bring on people who've done that sort of thing before.

Absence is the default for any ontology.