Ryze's Combo Potential

So, I own Ryze but rarely play him because he feels... dirty. Like Yi, just mindless spamming to win. I got him in ARAM just now, and was disgusted with how ridiculous his "combos" were. Maybe I'm misunderstanding something, though, so let me see if I have this right.

His passive lasts for 5 spell casts, but after 5 spell casts it triggers again... right? Team-fights never lasted long enough to check, so I'm not sure. There's nothing indicating a cooldown on his passive, though, so... either that's a big "clarity" screw-up or he can chain his passive almost indefinitely in a fight.

While his passive is active, spell casts reduce other spells' cooldowns by Q's cooldown... at 45% CDR (using the Cunning masteries and Ryze's needless free 30% CDR) that's 2.2 seconds. At 45% CDR, his spell cooldowns are Q - 2.2 / W - 7.7 / E - 3.8 / R - 16.5

Get 4 stacks in prep for the fight. So you start with R to chase them down and start your passive (free shield) - - - ( 0 / 0 / 0 / 16.5 ) Then you Q them - - - ( 2.2 / 0 / 0 / 14.3 ) Snare with W so they can't go anywhere for 1.4 seconds - - - ( 0 / 7.7 / 0 / 12.1 ) Q's off cooldown so fire it off too - - - ( 2.2 / 5.5 / 0 / 9.9 ) E for some AOE damage and damage ramping - - - ( 0 / 3.3 / 3.8 / 7.7 ) Q came off cooldown because shenanigans... also your passive procs again - - - (2.2 / 1.1 / 1.6 / 5.5 )

And then there's a merciful little window where your opponent can try to escape before the snare comes off of cooldown and the whole thing keeps going. Damage taken at this point: 740 + 210% AP + 16.5% Mana

W when you can, I guess - - - ( 0 / 7.7 / 0 / 2.2 ) Q is off cooldown (might as well not even give it a CD at this rate) - - - ( 2.2 / 5.5 / 0 / 0 ) Ult to make sure your movement speed, spellvamp and AOE damage doesn't end. It has a 6 second duration, btw, so it's probably never even stopped. - - - ( 0 / 3.3 / 0 / 16.5 ) Q again! - - - ( 2.2 / 1.1 / 0 / 14.3 ) E is available, so do that I guess, and pick up another shield from your passive - - - ( 0 / 0 / 3.8 / 12.1 ) Q because casting anything else will bring it off cooldown - - - ( 2.2 / 0 / 1.6 / 9.9 ) W - - - ( 0 / 7.7 / 0 / 7.7 ) Q - - - ( 2.2 / 5.5 / 0 / 5.5 ) E - - - ( 0 / 3.3 / 3.8 / 3.3 ) Q (passive!) - - - (2.2 / 1.1 / 1.6 / 1.1 )

And then the opponent gets another 1.1 second window of safety, before the whole thing starts over again. Damage taken in the second wave of the combo: 1160 + 355% AP + 26.5% Mana... total damage from both waves: 1900 + 560% AP + 43% Mana

Am I missing something here? Or can Ryze literally keep his passive AND his ult going continuously, as long as there are opponents to cast spells at? And it's not like there's a lot of fore-thought or strategy involved in this... It's literally "cast Q if you can, and then whichever spell is available, repeat".

Someone tell me it doesn't actually work like this, please. I want to believe...