"Inconvenience" is downplaying the impact of not letting adults use incognito mode to search for things.
Yes, right now search engines are only going to blur out images and turn on safe search, but the decision to show or hide information in safe search has alarming grey areas.
Examples of things that might be hidden and which someone might want to access anonymously are services relating to sexual health, news stories involving political violence, LGBTQ content, or certain resources relating to domestic violence.