Ap vs CDR for support items

I have been trying different support builds and have noticed that it is rather difficult to have a full build without going above 45% CDR. On the other hand support builds hardly ever have AP. The only decent ones i know off are that give AP and are useful for supports (not for mages in particular).

Just with these 3 i can have 45% CDR. Don't you guys think support items need more AP across the board?

Lastly i know that supports are not suppose to deal damage but supports have abilities i.e. shields and heals that scale with their AP. For instance did you know that for soraka 4x would be more beneficial for her heals than just straight up AP items i.e. . Also gives 20% shield/healing power but for soraka gives more healing power. The general idea here is that AP + % healing work well together and full AP or full % healing items are not cost-efficient.

Although 4x don't stack so that's not an option here. Then there are other scenarios where as a a soraka i would want AP i.e. if the enemy has burst they will always go for adc first as soraka cannot heal burst fast enough so i usually get but it's active has a rather high CD so it is not an effective method. Usually you would want to go more AP in these scenarios to increase your healing potential but as i mentioned above other than 2 items which give mediocre AP there are not enough AP for me as a traditional support to build.

is obviously great for healing but it goes back to square 1 where i don't completely want to rely on my items active plus i don't think redemption's active is used to counter burst in particular than it is to be used in compact team fights. Nonetheless some traditional supports like Lulu and sona would also benefit alot with some AP and not just %healing/ shielding item passives and abundance of CDR on them. What do you guys think?