I haven't looked into it, but accepting payment for that act is probably just as illegal as killing someone. So even if you can't get caught for the killing, they can put you in prison for accepting the money. We're only going by what the options actually give us.
Additionally, if you fail to make the killing (for whatever reason), you have to deal with the consequences of attempted murder, including retribution by the intended victim.
There's also no guarantee that this will be a lucrative business because even if you can't be tied to the killing, the perception of most people is that THEY could go to jail for hiring you, decreasing demand for that service. Also, you assume that there's a high demand for contract killers which I would guess there's not. Especially not among the high dollar clients who like to keep their hands clean and enjoy their money. The people desperate enough to want to kill someone probably won't be able to afford your services and if they can, you aren't making enough to become rich and famous.
I don't want to take so many risks. Ultimately, I'm only seeking money and fame. Might as well skip the steps to it. If you have money and fame, everyone else becomes irrelevant, even those you hate.