That's false, and can be trivially shown to be so with a simple hypothetical counterexample:

Imagine a system where ad servers sent 10 ads to your browser instead of one, and then your browser decided which ad to show you based on some settings you previously selected in your browser settings page. There you have it: personalization without privacy invasion. Easy.

Google's system will undoubtedly be a bit more complex than that, but there's no reason why it would necessarily have to invade your privacy just because it allows ad customization.

The system you suggest doesn't come near privacy. Sure, there is some uncertainty over which ad was shown, but as soon as it is clicked you have revealed that too. And it's clicks and page visits that buils visitor's profile, much more than ad views.

Obviously if you click on an ad then yes, the advertiser will know you're interested in that product. I don't see how that has anything to do with ad personalization though.

And with this system, the advertiser wouldn't have the ability to build a profile on the user, since the idea is to replace cookies with this system, not to merely supplement them.

If you are that concerned about privacy, why would you click on the ad?

Why would I want to see online ads that I can click on if I can't actually click on them?

Sure you can:

  <ad>
    <adsrc href="/ad/car" src="car.png" keyword="automobile">
    <adsrc href="/ad/pet" src="pet.png" keyword="cat dog pets">
    ...
  </ad>

Of course this "allows" ad blocking, so Google will come up with some reason to reject it, but it's a perfectly workable system.

so list all ads for every category under the sun in every page?

I guess it depends what you mean by personalization.

Putting an ad for sneaker-related products on a forum for sneaker-lovers, for example.