uBlock Origin will do this for you, if you want that level of privacy. You do have to specifically allow it to operate under Incognito Mode, but then it "just works".

Yes, it's an add-on and not built into Chrome... and yes you have to know about it to install it in the first place. I'm not exactly sure that's a problem though - if you are technical enough to navigate through settings menus in your browser, understand what the settings mean and toggle options (presumable to enable some built-in version of uBlock Origin), then you clearly have the capability to install the add-on.