Use free proxies and VPNs to get around IP blocking.
Make the primary purpose something else (e.g. quickly parse the results to make "art") and even add an anti-DoS mechanism that measures the response time and slow down if it increases significantly. The latter would make it less effective, so the sensitivity would have to be adjusted to not slow it down too much but still be plausible to say it's an anti-DoS mechanism.
Maybe we should go back to the throwaway accounts and spam idea. That would be more effective at draining the resources of spammers (who presumably have a lot more resources than ordinary home users, plus unlike Google do not provide anything useful to end users), which would also be a good thing. And it would use minimal resources on the client side.
You are still missing the point. Lets say that a ddos of google could work, and it wont, but lets say it will, what then? Does this stop every other website on the net harvesting data? No. I have a webserver, I own the physical box and maintain it, on it is 1 wordpress site, its colocated in a secure facility. I have never installed any analytics and I have no advertising and yet, wordpress or some plugin i am using is harvesting data all the time and I cannot stop it. And i just do not have time skill to write my own blog software from the ground up, so i live with minimal data harvesting.
But these are not even the most pervasive of issues. What about everytime you order from JLCpcb or Ali Express, your information is passed onto the Chinese Government, or at least can be as that is the law. And this goes on and one. Or what about your cell phone? Its tracking your crap all the time, its apps are reporting back to the mothership all the time, its gps can locate you to within 20m. A smart phone is nothing more than a surveillance device in your pocket. How about your smart watch? Yeah you are being watched all the time. The question is how much of that being watched actually matters? And just remember, your TV is watching you too.
The best any of us can do is to block as much as is possible and after that, avoid the internet, cell phones and other smart devices if you are actually worried. Consume less is the only way to not be a bitch to corporate interests. Personally, i do not care all that much about data tracking, my life is boring, i am not a criminal, i obey the law, i pay my taxes. They know i walk from my bedroom to my office in the morning and go to work, they know i shop on ebay, jlc, lcsc and mouser, visit the same bunch of websites every day and am not big on social media. And i am ok with that.