Arguably because the division produces a "shelf" for the tabs to sit on rather than just floating in the air with no clear relation to anything; the line also creates an overall container for the header content versus question list/sidebar below. In fact, the point at which you decided to fade the gradient out actually tends to end up associating the tabs more with the list below than indicate they're part of the header(they're somewhat related, but still a separate process/path from the active/featured/etc links.). That effect will be even worse on single-question screens where they're completely unrelated to the content below.
StackOverflow basically does what you're describing, though more starkly; compare how noisy it looks up top.