Not true, tanks aren't as useful in the beginning, and they can be made worthless from effective zoning and dives.
Likewise, pokers are good in the beginning and middle, but fall off at the end if you don't capitalize on the early advantage.
ADC are slightly weak in the beginning, and only scale upwards.
AP casters that don't have poke are strongest at early game and stay about even in terms of effectiveness as the game progresses, because they tend to have good late game scaling as compensation for their slightly weaker early phases.
And supports are always useful, so long as you can support a team effectively, and your team isn't batshit retarded.
What will ultimately dictate a game though is good cc.