Besides, with my approach you get a lot more flexibility. For example, it's trivial to adjust their reaction time; just adjust how long between updates.
There's still no reason to store the delay multiple times as a field in each instance, unless you're describing a system in which each instance's delay can be unique, in which case that's totally different to what we're discussing (because unique delay periods may well sync over a certain period of time and we're specifically trying to avoid that).
On the surface it looks like a straightforward mark of progress to go from updating every enemy every frame... to one enemy every frame... to one enemy every x number of frames. But if updating a single enemy is so time-consuming that you're thinking about not even doing one every frame then I'd stop to think how your game is going to look: Jerky, with one frame in however many taking longer to resolve than the rest.
In that situation I would bite the bullet, drop the frame-rate of the game down in line with the speed of updating one ai and go back to doing one per frame. There are advantages to keeping the load even, I think.