In Google Chrome’s “Cookies and site data” settings, accessible via the Preferences menu item or directly with
chrome://settings/cookiesin the address bar, you can enable the setting “Clear cookies and site data when you quit Chrome”. However, I’ve discovered that Chrome exempts Google’s own sites, such as Search and YouTube, from this setting.
I don’t want to sound like a broken record, but this really shouldn’t come as a surprise to anyone. Technology companies are particularly adept at being hostile towards users, and Google is no exception.