edit, i probably should point out at some time in this thread that I am an ad carry main. So part of this is indeed the whole 'rock is fine, nerf scissors'-paper thing going on.
I don't know, maybe not.
I'm typically a caster player in DotA (or I have been for most of my "career"), and I like how they dominate the early and mid-game.
Think about it: If you shut the enemy team down hard enough early game, it never makes it to late-game. You have the power, as a player, to direct the flow of the game from the very beginning. A carry can only do well assuming it makes it to late-game, and you're completely relying on your supports and casters in DotA for it to get there. That's why I said before, Int heroes in DotA are the most valuable asset on any given team, contrary to popular belief. The carry in DotA is kind of like the singer in a band; everyone gives him all the credit because he's the center of attention, but chances are he would never have gotten there without his team.
Because AP and AD are both powerful late-game, there's really not a role (that I've seen used) that excels early game; at least well enough to end it before the carries can get farmed. In LoL, you're pretty much forced to go into late-game in most competitive matches, which means that, like you said, it all revolves around your carries (AP or AD) and how much damage they can do. In other words, as an AD Carry in LoL, it's much less interesting and challenging (in my experience) than in DotA, because in the end everyone is going to be as powerful as you anyway; which isn't the case with DotA. It's also why, in my opinion, LoL matches are often so much slower than DotA matches. You're trudging through the early and mid game, waiting for your carries to get farmed.
I was watching some tournament play yesterday for League and DotA. I think the League Tournament was the IPL5 and the DotA tournament was WCG 2012. Anyway, the League game I watched ended with the total killscore being about half the game's duration (so it was about 22 kills at around 40 minutes). The game was probably over long before that.
The DotA 2 game had about double the kills of the game's duration (about 60 kills at 30 minutes). Sure, it's anecdotal, but this is the kind of trend I usually see when I watch competitive play for either game. I personally think a big reason is because DotA has roles of heroes that are powerful at all stages of the game, and can
win at all stages of the game, where most of League's power is skewed towards the end-game.
Neither of these things are good or bad per se. Some people like a slower paced game.
I used to play Veigar a lot, and I found that his ability to farm AP all game, then crunch people at the end was a lot of fun. Even though he didn't fit into the traditional "DotA" role of what a caster should do, he was different than the typical LoL caster in that getting farmed meant having good positioning, getting lots of last hits, and he had a really interesting AoE stun field that could really turn the tide of fights. Even though he still wasn't very good early game, he had a unique caster playstyle that was about more than just doing damage, damage, damage.
Ironically, around the time when bruisers started becoming popular (which was a couple years ago at least), he just fell out of favor, and has never really returned. The problem is that there's really only 1 AP Carry, and the support player doesn't have to build AP (think Taric or Leona). Even the AP Carry, realizing he's facing a Veigar, can do all kinds of things to counter him. He can go a tanky AP build like Rod of Ages (or something similar). He can Banshee Veil. He can get Zhonya's and just "dodge" your entire combo.
Nuanced casters like Veigar have no place in the game. What is Veigar going to do against a bruiser? Answer: Nothing (unless you count dying). He's Tier 4 in Elementz Tier List for good reason. The best casters are just the AP equivalent to carries.
