Ludens has movespeed which synergizes with running around to charge proc. Cool. But there are NO items that offer just cooldown reduction and AP without the mana regen (or attack speed) which a lot of champions don't need.
AP + Mana Regen + CDR items:

AP + Attack Speed + CDR items: 
AP + CDR, not Mana Regen/Attack speed:
and all Runeglaive items
No AP + CDR items? I don't follow...
And wouldn't cdr synergize with the ludens passive better than the move speed?
No, you most certainly do not proc Luden's only every 10 spellcasts, or even close to it. Most champs do it easily every cycle, as they run around waiting for it to return. Ryze and Cassiopeia are basically the only exceptions to this, but even they rely on being far too sticky to use it as a typical mage.
The funny thing about the Luden's nerf was that they actually thought dropping to 10 charges per spellcast did anything at all beside maybe delaying combos by 30 movement charges, which isn't much at all while waiting for cooldowns anyway.
Nashors on the other hand does have the cdr. But how does that make sense? It's an item that encourages auto attacking. What synergizes with auto attackers? Move speed (Although what doesn't move speed synergize with? Come on main it makes sense on nashors though). Nashors could basically be an ap version of zephyr minus the tenacity.
Generally, Nashor's is allowed to have conflicting mechanics like Attack Speed and Cooldown Reduction because no one does use them together properly. It allows such items to be more gold efficient than their non-hybrid counterparts. Somewhere down the road, however, the hybrid fantasy got lost, and this item (along with Guinsoo) kept falling further and further behind.
These items are supposed to be strong early items which heavily help champions right away, but then after that grab, choices need to be made to make them viable into lategame. Superstacking stats is not as viable on anyone who starts hybrid, such as AD + Armor Pen + Crit + AS, or AP + MPen + CDR. The early power is supposed to make up for the late issues, but that hasn't been the case in a very long time.
A champion that may be hurt by this change is Kayle, as she'd need to find another source of cdr for her ult and to have 100% up time on her E. However, if this change were implemented, then perhaps they could give Kayle some power back to compensate via more damage or making E decrease in cooldown with rank.
Well, she could always use one of the other numerous CDR + AP items available. She may even work better with the Mana Regen, as her W really weighs down her mana expendatures.
And overall on Luden's, that item is a cancer because it is made to replace a cancer. Dropping MS isn't going to do the trick, as it's imitating the Lich Bane which dropped heavily on its stackability many patches ago. Luden's may not have the potential damage of Lich Bane, but the higher reliability on spellcasters as well as the obscenely high AP tagging along is what makes this item particularly a cancer. Highest AP in the game plus free damage on top of it was never going to be healthy. Just adding CDR like Deathfire Grasp had won't make any difference on a burst champion when running is a more effective charging mechanism anyways.