The obvious answer is performance. But I find that in order to make both the red notification icon at the top left and the blue notification icon on my responses tab go away, I have to click around to the item that caused the notification twice (accessing once from each method). Even if I am on the item and hit refresh. The result is that I am constantly wondering whether the notification I'm seeing is a new one or one I've already seen.
Your experience isn't entirely as it seems (or at least shouldn't be). As soon as you open the StackExchange™ MultiCollider SuperDropdown™ or view the responses tab, the notification icon on each respective control should disappear regardless of whether or not you actually go to the relevant notification item (although in the former case, some people wished things worked a bit differently).
As for why you have to clear them independently and deliberately, I'll refer you to this answer by Kevin Montrose:
The responses tab and inbox show slightly different data.
The inbox doesn't include revisions, and the responses tab only shows activity on the current site. Viewing either clearing the unread count on the other would be incorrect.
...as well as this one.