Maybe you can't split ads from search, but you could totally split Google Cloud | Search + Ads | Youtube | Maps -- and who knows what else google makes profit with.
The effect on YouTube may be interesting and actually end up more beneficial. They could still run ads based on the videos you are viewing, but maybe they'd have to make up lost revenue by getting more people to pay for subscriptions (e.g. YouTube Red). Those subscriptions would signal to YouTube which users have expendable money (especially if it's a tiered pricing system), and what channels and videos you as a paying customer actually value spending money on. Some of that money could be used to increase payouts for content developers, hopefully increasing quality and user retention, ultimately spurring a positive cycle.
