On the front-end side, the cookie setting takes up some of the precious bytes that get transferred before the browser can start downloading assets.
I have turned off everything I can turn off that adds cookies to ExpressionEngine's output, but there were still two cookies hard-coded into the output even for logged-off users:
The code that does this is in
$this->EE->functions->set_cookie('tracker', serialize($tracker), '0');
$this->EE->functions->set_cookie('last_activity', $this->EE->localize->now, $expire);
Note that EllisLab staff says making this change "can affect your ability to upgrade, and your ability to receive support." They also point out that you would need to re-apply such changes after an upgrade.