Since stab hits are now pretty dire you will almost never see an AI DOW without a CB as was so common in EUIII.
Never happened to me in EU3 and yet in EU4 AI will declare wars without CBs with impunity, especially on the PC. Check the logs in game and you'll see them regularly declaring wars without CBs and with royal marriages without a care in the world, because they do not get stability hits, so this talk of them 'using reserves to boost back to 3' isn't true.
Get a scenario where a country will declare war on you with a royal marriage or without a CB, in a situation where they should get a stability hit. Tick 1: No war. Tick 2: X declares war on you! [With or without CB] Tick 2a [without unpausing after the declaration of war]: Check stability of computer nation. Will be the same as Tick 1.
Stability hits are taken into account the second you declare a war, and the AI works in 'ticks', so it wouldn't spend any points to boost stability until Tick 3 of this situation. If the stability is the same as the moment they declare the war, they are not getting a stability hit. I know it's hard to believe but the AI in EU4 does not understand the simple mechanics of the game and therefore ignores them.
Readily admitted by the paradox crew that they don't know how to make an AI to be able to play their games with competence, as well. The quote is something along the lines of "The AI doesn't understand how to prepare ahead of time so we just let it ignore x!' where X is any penalty/malus incurred on the player for simple actions of progress.
It doesn't matter how neat the mechanics are in this kind of game if none of the other colors on the map know how to utilize them and outright ignores mechanics the player is forced to utilize.