Some disorganized thoughts:
* I worry that waiting for my opponent to calculate points for half their army immediately before the game could be prone to taking a long time (depending on indecisiveness) and possibly increase the likelihood of list-writing mistakes.
*
CP costs to add new detachments that in turn cost
CP seems like it could really exacerbate that first point.
* How would this interact with built-in deepstrike mechanics and deepstrike stratagems? Say I add some swooping hawks to my list with this method. Swooping Hawks are significantly more useful if I can deepstrike them in rather than having them show up along the board edges.
* I feel like a more conventional "side board" might accomplish roughly the same thing while being less prone to severe list tailoring or time consumption. Maybe something like:
Side Board (X CP)
Use this stratagem when assembling your army. You may include up to two SIDE BOARD detachments in your army list.
After revealing army lists but before deployment, you must select a single SIDE BOARD detachment and declare you'll be using it in the game. If your opponent is also using SIDE BOARD detachments, roll off. The loser must declare which detachment they'll use first.
Only the SIDE BOARD detachment you actually use in the game counts towards your total army points, starting CP, etc. Your warlord may not be in a SIDE BOARD detachment. A SIDE BOARD detachment may not contain more than half of your total army points.
This stratagem costs 1 CP per 200 points in the SIDE BOARD detachment.
So similar to your suggestion, but you have to do all the list building before you show up to the table. You could have an anti-tank side-board and an anti-infantry side board, for instance, but you wouldn't be spending 15 minutes cooking up the perfect counter to your opponent's army. And because there's not strategic reserve limitation, you don't have to worry about lowering the value of things like artillery pieces that want to be shooting from turn 1.