Prior to getting glacial shroud, which many Ryze's will wait to build until after getting tear, t1 boots, and a catalyst for survivability, ryze won't have much CDR. The CDR from blue will help a lot.
If Ryze is facing a champ that is pushing them into their tower a lot, blue is EXTREMELY helpful, because it allows Ryze to push the wave back without running oom.
I like getting blue even after I have my shroud (if I don't think anyone else needs it more). You can spam your skills to charge your tear (if you do that without blue, you go oom fast). You can clear waves very fast/push your lane. You can keep someone pinned on their tower so you can go gank. Etc.
Later on in the game, Ryze does not need blue. But it is still nice to have if you can get it. Don't go out of your way to grab it if one of your teammates can get it, but if you have an opportunity, and no one else on your team who can use it is around, definitely pick it up. The people who say Ryze has infinite mana at end-game are incorrect.
Q costs 70, W 140, E 120.
Is 6 Qs, 2 Ws, and 2 Es.
That is 420 + 280 + 240 = 960 mana.
So a full combo takes almost 1/4th of your mana.
How much mana regen do you have? Well, you have an archangels staff (if you have completed your full build) for 25 mp5. And thats it.
And if you haven't fully finished your build (which costs around 14.5 or 15.5 depending on which items you get), you only have 7 mp5 from your tear.
And then another 3 mp5 from masteries.
And at lvl 18, I believe Ryze's base mp5 is 10.8.
So before you have a full build, you get 20.8 mp5 (assuming you don't have mana regen runes), which is 250 mana per minute. So if you are out of your base for 4 minutes, that nets you another full combo.
So you can do about 4 full combos before running OOM with 4k mana, plus another full combo for every 4 minutes you are out of your base, late game.
Once you get archangels, you get 25mp5 instead of 7 from it, for an additional 18mp5. Now you get another full combo for every 2 minutes or so you are out of your base, instead of every 4 minutes.