I'm going to make a counterargument here. Adcs have one cdr item from BF, and 0 from zeal. They have low cdr outside of ezreal.
Tanks are in an odd situation. Their CDR is allocated awkwardly. Tanks that don't use a resource (zac/shen) you get dicked because almost all cdr tank items have mana. There are also a lot of non cdr tank items though. You may end up with not enough cdr in certain builds.
Mages do indeed have a ton of cdr. Many side items provide cdr and their cores all have 20%. Champions that use rod/rylais/liandries feel like shit because the more brusiery mage core build has none. It can be hard to cap in cdr for some builds actually.
Bruisers and juggernauts - Triforce or cleaver. Shojin champs hit max with 2 items. Others will get it through tank items or offensive items like DDance. Items like sterak/titanic slow capping quickly down though, you aren't gonna be at cap until later in the game in many situations.
Assassins can hit pretty easily, as they pretty much all can just do dusk>ghost>cleaver. They have pretty binary build paths right now so them very easily capping is true.
Now, WHY is capping more easily available than before? It makes the game easier to balance. While I do think cdr should be allocated differently than it is now, there's a reason they try to make capped cdr more frequent. The game already gradually becomes harder and harder to balance, trying to balance champions around super high stat but no cdr builds AND cap cdr builds only causes more issues than trying to balance around all viable builds coming close to or capping in cdr.