(Note: Not commenting on Cass specifically, but rather on the general concepts being discussed here.)
How is CertainlyT's post getting downvoted for discussing early/late tradeoffs and variant types of power curves? This is completely standard.
Linear warriors, quadratic wizards, and cubic carries.
If you make a Champion with insane scaling also have uncommonly strong starting stats, they're simply OP. You pay for the high ceiling with a low floor.
Example Power/Gold Curves
A while ago, I plugged some numbers into a DPS calculation site and computed these DPS values. (Note: Janna's DPS is not where most of her power comes from. The graph might make it look like Janna is much worse, but remember that she also has really powerful utility that holds about constant all match. This makes her stronger early. She has a high floor and a low ceiling.)
http://i.imgur.com/2xG0jby.png
http://i.imgur.com/BADq6G1.png
http://i.imgur.com/OyD4uCk.png
This fits with theory. (Okay, technically the graphs above are an order off the "classical" statement, but they also don't account for CDR and such.) Supports, especially back in the days of extreme Support starvation, held their role because they had the most "base power" of any Champion. A level 1 itemless Blitz hook is remarkably close to a level 18 full-items Blitz hook in its basic effect. (Contrast: an Ashe auto at level 1 with no items versus a fed Ashe level 18 auto.)
Mages are decent in the early game and peak in the midgame before falling off relative to carries.
(AD) Carries have a trashy early game and a mediocre midgame, but have the highest scaling of any Champion. They're literally of a higher order: they multiply more factors together. Attack Speed and Attack Damage don't independently increase DPS, they synergistically increase it: It's AD * AS, not AD + AS. That means that you get the most bang for your buck when you evenly distribute these stats, with their various coefficients in mind. (As with any optimization problem, e.g., to bound the largest rectilinear area with a given length of fencing material you use a square.)
For a numerical example, take a pile of points and assign them to the following formulae, into any of the variables. (I'm simplifying a bit with the orders, because of how this seems to work within the specific bounds of gold/items attainable in a LoL match.)
Support: 50+.5x
Mostly constant power, from non-scaling or low-scaling utility like most CC.
Mage: .1*x*y
AP and MPen multiply each other's effects. (CDR being left out for simplification reasons.)
Carry: .01*x*y*z
AS, AD, and Crit all multiply each other's effects. (Omitting ArPen, as with mages and CDR, to keep it simpler. The overall picture is the same.)
At 25 points
Support: 50+.5x --> 63
Mage: .1*x*y --> 14
Carry: .01*x*y*z --> 5
At 50 points
Support: 50+.5x --> 75
Mage: .1*x*y --> 63
Carry: .01*x*y*z --> 41
At 100 points
Support: 50+.5x --> 100
Mage: .1*x*y --> 250
Carry: .01*x*y*z --> 359