There are some famous examples of this working. But only because the parents had time, money, and high standards. Yes, not necessarily, and that's not all the story!
Proper home-schooling is a tremendous time commitment. It requires either a stay-at-home parent or dependably scheduled shift work. Even with lesson plans prepared by others, the home-school parents must spend time preparing and managing their child's education in addition to the face-to-face teaching time.
Money is rather irrelevant in many states. You can spend piles of your own money on a prepackaged curriculum if you wish. That is much less expensive than private school tuition, which is a big reason home schooling became popular (the benefits of a Catholic school education, without the tuition bills--or nuns). But you can also enroll in "virtual academies" that operate as charter schools in most states. They use the charter school funding to pay for the materials, certified teachers to assist you, and the required standardized tests. This comes at no additional charge, courtesy of your school taxes.
High standards will help you be successful. I think it's more accurate to say you should have motivation, meaning that you have standards consistent with your child's abilities, and consistently require those standards be met. Not all will be superstar students, but all can learn the discipline to do their best. That is the best predictor of success and happiness I know of, no matter what path your child follows.
You left out a key factor: patience. If you don't have the ability to stay with the program, to keep working with your child until he "gets it ", you will not be an effective home-school parent. The same is true for traditional teachers: the ones who don't care enough to persevere through the tough parts are poor teachers, the ones who treat the setbacks as opportunities are following the path of Jaime Escalante.
What I'm saying boils down to this: it's not whether home-schooling is right for your child, rather it's whether you are are the right teacher for her. If you're not willing to make the commitment to be that teacher, please don't home-school. You won't be doing your child a favor.