Would depend how they work, but assuming we're using conventional technology and not some magic doohickey that can 100% verify the truth, then you'd probably just get shunned by your peers. Technology cannot accurately verify whether someone is lying unless it's about an objective fact, and even then, its database may be out of date when someone's informing you of a new discovery. If you're using an LLM, then it may just make random shit up. And if you're using a corporate LLM, then you're transmitting everything you see and hear to some corporation, where they may keep that data for whatever they please, simply so you can have a popup that tells you either a lie itself, or something you should be able to surmise by yourself. You're not a corporation, so likely people wouldn't revolt against the glasses like they do against Facebook's, they'd just stop talking to you.

Because it isn't relevant, at all, and that is what downvotes are for.

Isn't the idea at least interesting?

Sure, if you're asking what to write in your next fantasy novel. This topic is about reality.