WordPress' own cookies can be disabled by commenting out three lines in wp-comments-post.php (except for the cookies set for registered users, which you wouldn't want to remove). And if your website has disabled comments anyway (which a few of mine have), then there isn't even any need to do that.
I agree with you camu, it's quite difficult, and you have to be picky about which plugins you use. But it's not impossible - I'm now running several totally cookie-free WordPress sites. Switching from WordPress Stats to WP SlimStat is one of the changes I made to achieve that. And this is going to become more and more common now, as more people start complying with this law.
The way the law has been implemented has been a bit of a mess, as lawmakers had no idea of the scale of the cultural change they were asking for. As a general rule, everyone hates change, and webmasters are no exception, so there is a lot of complaining going on. But I do think that website owners should be honest about cookies and tracking, and until now, many of them have taken it for granted that you don't have to be honest about them. So once we've got over the initial shock of the change this legislation will have a generally positive effect. Once we're through this, the next stage is to get websites to be honest about third-party scripts...