And how do you propose this to happen? Cp maps by nature have points all over the map, so separated spawns for red/blue will always result in an advantage for one or the other.
Fixed crazy king at point A start! Regardless of asymmetric spawn (which is okay - see Dota), the first objective is always central so roughly equivalent for both teams.
If we want to make crazy kings different instead of deterministic, then after the first point, it is a random chance whether this crazy king will go alphabetical (ABCDE) or reverse-alphabetical (AEDCB).
This way the second point is random so players all fight for A, and after that they can get their strategy together.
Plus this way crazy king is actually "crazy" instead of always the same.
I am OKAY with post-start spawns being next to active points, because each "side" has a different set of "good" points, and this promotes strategy. With my plan of random point order, the advantage should shift between sides each match.