Used to be that you had control over how your display URL was shown, less so today. As Netmeg said, the www is added automatically when displaying ads. But before they did, it did seem to make a positive difference in click rate when the www was NOT there. They also now lower-case the domain name part.
However, I noticed that it seems to be the reverse today. Small test but two identical ads except for the display URL: one with the www, one without, words in URL capitalized, just the domain name. Doesn't make sense but the ad with the www has a higher CTR, and by a good margin too that it can't just be by chance.
The only thing I can think of is that search partners may respect the capitalization and structure and this affects the data. Haven't checked it out but will soon.
Never did comprehensive tests when adding keywords after the domain but good point that it may be cluttering with no benefit. Although my instinct is to make it look more like a natural link.