Clean up your link profile or just disavow links?

In a recent video Matt Cutts introduced the link disavow tool. In very short words, this tool gives web masters the opportunity to basically tell google: “here is a list of links that are spammy and that I could not get rid of”.
So why do the tedious clean up work at all? You could just go to your webmaster tools and disavow the links instead of trying to remove them. Is that a wise idea? Is it possible at all? Caution! There is a little sentence in that video that many might have ignored. Google is going to do a before/after analysis of your link profile regardless of any disavowed links. Only if there is a difference google will see your efforts in really trying to clean up. I would consider the disavow feature as only a last resort if there are links that you can’t get removed even after trying to contact the other webmaster several times.
Last but not least, for whom is that tool? I would only consider using it if I got an unnatural links warning in my webmaster tools. I would certainly not use it as a preventive measure as that might even trigger a manual review when up to now there only was an algorithm ranking loss.

Here is the complete video, so you can make up your own picture: