Because choosing posts to honor in this way requires input from the community, this can't be automated. Except for two exceedingly-rare cases, all badge awards are automated and I don't see that changing.
Because the community needs to be involved anyway, this is an ideal thing for communities to self-organize. You linked to a one-time example; some other sites run quarterly "best answer" contests, with nominations and awards driven by the community. The winning answers are not necessarily the highest-scoring ones; sometimes they're in obscure areas that just didn't interest as many people but are nonetheless excellent. We've all seen cases where a quick low-effort answer to a popular question takes off (Hot Network Questions in particular), so this can't be score-driven. As an alternative, at least one site holds an annual bounty event.
Communities can and do self-organize to reward quality content. Instead of looking for a mechanical system-wide reward that would probably not highlight the stuff that ought to be highlighted, look around at what other communities are already doing and copy, adapt, or invent systems that work for your own community.
The two exceedingly-rare manual badges are Not a Robot, for attending (larger) events with SO Inc. presence, and a badge for discovering and correctly reporting certain security issues. I think this second one is retired now; I didn't find it on the badge list.