Players declare actions all the time in D&D, I'm not sure how you would run combat if you didn't allow them to declare actions. At the same time, I sometimes prompt them for saving throws or question whether they want to use a reaction in combat. I don't see why I would run out of combat scenarios any differently.
A declaration of an attack requires, at minimum, a target and a weapon. The declaration of the target communicates the goal: kill the target (or knock them out, which you would also need to specify as part of the declaration). The declaration of the weapon communicates the approach: by hitting it with the weapon. Therefore, “I Attack the orc with my longsword” is sufficient information for the DM to determine whether or not a dice roll is necessary to resolve the action - which it may or may not be! For instance, if the target is immune to damage from nonmagical weapons, I won’t bother calling for an attack roll if the attacker is using a nonmagical weapon, because there is no chance of success. If the target is incapacitated, I won’t call for an attack roll because there’s no chance of failure.
I don't see any distinction between a mental activity and a physical one. If I'm having a discussion with someone I may be studying them closely, listening for pauses or lines that sound overly-rehearsed. In other words, making an insight check. The phrase "can I make an insight check" indicates something the player thinks their PC would be actively doing.
See, “studying closely, listening for pauses or lines that sound overly-rehearsed,” that sounds like an approach to me. What’s your goal? What are you trying to learn by doing this? The answer will have an impact on whether or not you need to make a check to achieve that goal with that approach. “Insight check” is neither an approach nor a goal, it is a means of task resolution.
If someone declares they want to use a skill and it's not clear*, I'll ask for a clarification.
*
Although I do have to question how "I make a thieves tool check" could be unclear. What else are they doing if I just told them the door they're trying to open is locked, using their tools to braid their hair?
“I make a thieves tool check” is sufficiently clear. It communicates a goal (open the lock you’re picking) and an approach (with thieves’ tools). If a player declared that as an action at my table, I would say, “sure, that’ll take 10 minutes and a successful DC X Dexterity check, with your Thieves’ Tools proficiency of course” if the lock could be picked and there was some kind of time pressure. If the lock was beyond the character’s skill to pick, I would say, “no need, you can’t pick it.” If it could be picked and there was no time pressure, I would say, “no need, you’ll eventually get it open.”
If the DM does not allow players to ask for insight checks and only calls for insight checks when an NPC is using deception the players will pick up on this pattern quickly. If the DM does not call for an insight check after talking with the NPC, the players know the NPC is telling the truth. The players are getting a free "zone of truth".
I mean, detecting lies is not the only thing Insight can be used for, and like any check it is only called for in response to an action (with a clear goal and approach) that the player announces. So, I don’t agree that any discernible pattern will emerge from when the DM dies and does not call for a Wisdom check. The only information you gain from the DM calling for a Wisdom check to resolve your action is that it is possible, but risky. to achieve that particular goal by that particular method.
Last, but not least asking both Bob and Susan for insight checks is dictating what their PCs are thinking and doing. Only Bob and Susan get to do that.
I wouldn’t ask them both for Insight checks unless they both announced actions with possibility of success, failure, consequences, etc. so I’m not sure what you’re driving at here.