His gimmick is spam
He's gated by mana
Once he builds Tear he has no real gate anymore. Plus it contributes to his damage.
Cassiopeia also spams her abilities, but that isn't her "gimmick". Additionally, Ryze's cooldowns are implemented in a way that even at 40% CDR there is a brief gap in between his full rotation. At lower CDR values in the early game the gap is more evident and the lack of mana deters him from spamming his abilities. At level 6 he has 497 mana + 250 (tear) + however much he's stacked thus far. Suppose we're at a flat 750 mana, and we are wave clearing with EQ (80 mana), we would only be able to use EQ 9 times in lane before we completely run out of mana. In the early stages of the game at least 3 EQs are needed to completely clear the wave, but I don't even do that. Therefore this is the time to capitalize on Ryze.
He's gated by mana
Once he builds Tear he has no real gate anymore. Plus it contributes to his damage.
Tear and mana in general, prior to completion of Seraph's Embrace, marginally influence his damage. Briefly looking at his Q ratio, 3% bonus mana isn't all that much, especially in the early game. Suppose you have Tear (250 mana), 3% of that nets you 7.5 damage. Even in late game when you have 2500-3500 bonus mana, the damage ranges from 75 to 105, respectively. After you incorporate resistances, the damage further decreases.
He has no ult reliance so all of his damage is in his base kit. It's almost like Udyr where since he effectively has no ult more of his power budget goes into his base kit
I'm sure you're away that Ryze's Q damage is amplified per R rank. The scaling goes 40%/70%/100%. The Q amplification used to be on Q, but they shifted the passive to R to add incentive to invest in it. So now, he obtains full damage at level 16. The primary use, however, is a great roaming ability. You'll only understands its capabilities when you use it as much as you can. You'll understand its range and how you can clip over walls with it. It's extremely useful and reliable.
Not that hard of a problem to figure out. Now that he no longer needs to spam E to get his waveclear that ability needs an actual cooldown at its early levels. there are too many relics from when he was a combo mage that aren't needed anymore.
Not sure why you you're saying that Ryze doesn't spam E anymore. In fact, Ryze uses E more now since he can apply E-flux to the entire wave. Before his E was changed, he could double E, wait for E to almost come off CD, Q the wave, then E again for it to double bounce off the Q, then if needed Q again. I could do this with tear + 2 sapphire crystals in the early game at level 6. The net cost was 200 mana or 240 if you used the 2nd Q. Wave clearing like this was faster than it is now but it cost much more mana. So they made is "easier" to wave clear by making flux spread but removed the double bounce mechanic.
