There's a difference between Google Analytics and Google Adwords. Two different interfaces (that can be accessed more or less in the Adwords interface once the user's Analytics account has been linked in the Adwords interface, but it's still a separate section, and the Adwords conversions show up in the Adwords stats, or can be viewed via Google's My Client Center). Different code.
Also, we need a way to integrate Bing's conversion code, too.
As WordPress moves more in the direction of whole websites and not just blogs, and especially if e-commerce is involved, we need a really easy way to integrate the analytics, especially if we have a variety of conversion codes.
You suggest adding some code to the header.php, but what if we have several different conversion codes for several different forms? There's only one header.php, right?