Well, ideally yes, but let's be honest here. If we can't trust websites to not abuse data, how can we possibly trust them to respect a polite request not to gather the data in the first place? I would personally rather have an incognito mode feature that I have confidence performs the task it claims to do without alerting the website, than one that loudly announces its presence, on the hope that it might be respected.

I don't trust Google, but I certainly don't want Google to trust random websites on my behalf.