Breaking out the ad business doesn't mean selling it, it means creating red tape through layers of indirection between the ad business and the rest of the company. In essence, this would be no different than the split between Alphabet and Google (or Waymo, even): https://www.kamilfranek.com/what-companies-alphabet-google-o...

"Pulling out" would be a massive blow to Google's revenue and shareholder value, even compared to the massive costs of restructuring the business to comply with the breakup. It would be economical suicide and career suicide for the CEO.