I guess I've never really considered an Insight check as "a described action." It's something that happens in the background at my table.
Like, for the "searching out a lie" part of the rule. Let's say that there's a conversation between one of the characters in the group and an NPC fisherman, and they are talking about the fish that got away. I might ask someone at the table to roll an Insight check to see if the NPC is being sincere, exaggerating a bit, or outright lying to them. It doesn't cost the character an action, and they don't have to declare it, I just use it as a way to shape the tone of the scene. My response is always something like "the fisherman really believes what he's saying," and never "the fisherman is telling the truth."
And for the "predicting someone's next move" part, I ask a player to roll for Insight in combat to help the party understand their opponent's behavior and to build tension. For example, if their enemy readies an action, or a dragon's breath weapon recharges, I'll ask someone to make an Insight check for free to see if they notice. It doesn't cost the character an action, it's just a way to measure intuition. It's something I do to build tension.
Players that ask for an Insight check are usually doing so because they don't know what questions to ask, or they don't know who to trust, or they just want to resolve a complicated social situation with a single dice roll. And that's...not really what the Insight skill is for. So I consider it to be a request for more information...they are saying "um, could you give us a hint here?" I'll let them roll, but I'll ignore the result and give them more hints about questions they should ask, or which NPCs might be more trustworthy, or what they should expect, etc., to help them move forward.