The general idea of making these notifications more subtle is that they aren't as actionable as the red inbox notifications.
When another user leaves a comment, an answer to your question, or a chat message, these are items that may require follow up on your part, and sometimes a certain outcome may very well depend on how quickly you respond to that inbox message.
As an example, let's say another user leaves you a comment pointing out a massive error in an answer you just left on another question. Since the red inbox icon is attention-grabbing, your chances of responding to the comment by fixing the error in your answer may very well save you from losing precious reputation and also prevent more people from being exposed to potentially misleading or incorrect information.
Now, take notifications, for instance. These messages are for things that don't require any action on your part. The message about your Silver Enthusiast badge could sit there for days before you notice it, and no matter what, the outcome is still the same.
Sure, maybe you don't get to celebrate right away, but you'll still be just as pleased with yourself whether or not you find it sooner or later.
If you're a user on the site who posts a lot of comments, asks a lot of questions, posts a lot of answers, and participates in a lot of chats, then you most likely get lots of those red inbox alerts. If those same inbox alerts were accompanied by system notifications, then they would reduce the importance of the inbox notifications.
However, when checking an inbox notification, there's a very high likelihood of also taking notice of the system notification, but without diluting the importance of the inbox alerts.
In summary, the primary reason behind the subdued notification alerts is to reduce the amount of noise and distraction that prevent us from focusing on the things that require our attention.
With that said, could we suggest a better color? Black? A darker grey or green? Absolutely, but it shouldn't be a louder color than what's used for the inbox alerts.