You can use a Crawler Poison bear trap to immobilize+stun someone in a chokepoint for 5 turns total.
4 turns. Crawler poison kicks in after 2 turns and lasts for 2 turns, one turn of bear trap immobilization is effectively lost.
The only thing you're doing is nerfing a fun ability into being unfun by tying it to a huge cooldown
Right now Quick Tinkering allows the player to keep an enemy immobilized for an unlimted amount of time because the cooldown is lower than a bear trap's duration. A cooldown of 4 or 5 turns would prevent this. How would that make this ability unfun? Unless you spam it every 2 turns to keep enemies stuck in place for the entire fight, it shouldn't affect your playstyle.
What that should lead to is enemies detecting your traps if they are able, and turning a corner to enter cover and stay there if you try to do any rubbish like that, which would leave you to end turn until combat ends and go disarm your traps, which would instantly train you not to do said rubbish in the future against intelligent enemies.
And how is the AI supposed to figure out when it's a good idea to hide behind a corner and when it's not? What if I WANT them to hide? The point of cutting off a part of the map is obviously to fight a single enemy/group of enemies without worrying about others coming to help them, so it's beneficial if they stay behind a corner in this case. An incomplete circle of traps could act as a saferoom in case the player gets low on HP, just get inside and close it with a single trap to make enemies run away. It would still act as a permanent Force Field, just for different purposes.
Or what if there's no corner to hide nearby and I have a sniper rifle? My point here is that unless you make a really sophisticated AI, being able to permanently block tiles is always going to be prone to abuse.