This graph might make help clarify somethings.
Position of LoL lines relative to DOTA lines means nothing, I just put them on the same graph for easy comparison.
This is assuming all heroes involved have an equal amount of farm. As you can see, casters fall off fast as they approach 16, but have much greater damage growth early on. Carries, on the other hand, never stop scaling with their farm. LoL is similar, but the disparity is less extreme, which is why Annie will need as much farm as Yi to be able to melt faces.
Gold loss on death in DOTA somewhat justifies the difference in power growth, because casters have a huge advantage over carries from early game to mid game. Most teams are made up of casters. A carry is only a win condition, casters are the real backbone of the team.