You don't deactivate all cookies as such, you deactivate personalised tracking cookies.
So the site shouldn't place a cookie 'session_id=12345678', but a cookie 'techcrunch_tracking_enabled=False' that's not linked to any particular user would be just fine.
And you don't think they really stop tracking you just because you said you didn't like it, right? What would you even do against it? Sue each and every website owner on the planet somewhere in the EU where they might not even care?