Why does being the first person to answer a question (which is accepted with score 10 or more) merit a silver badge? This seems like a quite arbitrary requirement to me. Is it just to incentivize people to answer questions quickly? In my experience, most good questions get answered within an hour or so anyway.
Participating in the SE has to be fun otherwise people won't do it, and earning badges is part of the fun. As the recipient of a few Enlightened badges they have always felt like a thank you from the SE for the effort I put in, and actually I like that - it's always nice to feel appreciated.
I don't think the Enlightened badge is intended to stimulate answers because it's hard to plan for it. If you jump in with a quick answer in an attempt to be first then you risk being trumped by a better and more considered answer later. I suppose the badge might incite you to jump in quickly to be first then rewrite your answer at leisure to make it better. If it ends up with a good answer for the PSE then, well, that's all to the good though I can't help feeling that anyone intent on this strategy really needs to get out more.