He starts off with few assets. He is still the smartest man on the planet and wipes out a solution for basically every problem in a matter of moments. And he is a respected, and feared, member of the world's Supervillain community. Even with his legal issues, he has access to Lex Corp and its technology. He is temporarily inconvenienced.
Yes. He is built into the universe. However, this also means that in some situations, people might complain about "That isn't how the character should act!" (like, say, Catwoman running a brothel with mind controlled girls. Especially if one goes with her dominatrix backstory) A character being built into the universe is not inherently good, nor inherently bad. It just means that the character is not an OC. That, however, also means that the character should act like that character. And in case of, to continue with Killgrave, that would mean "total asshole". Which can be fun... But others might not enjoy being railroaded into "ahahaha kicking the dog is so much fun!" Asshole.
No. The charm of playing a "random schmuck" is to actually rise through the setting, while giving more freedom to how the character acts, while having more freedom with how the character acts than with an established one.
Heck, the vast majority of, say, Naruto games have you play OCs (usually with some sort of mind control powers or something like that, admittedly) instead of the title character because it allows them to approach stuff differently.
And as I said: Working for the achievement tends to have a better pay off. I genuinly think that starting out low on the pecking order and having the character have to work for the rise would be a more interesting story than "Hey, I am Dr. Doom who's currently slightly down on his luck, but after an hour, I am set and have the top heroines captured!" or "Hello. I am the Purple Man. AFter 50 minutes, half the important heroines are my pheromone addicted, brain washed cum dumps!"
