Einstein comes along and says, space and time can warp and curve, that's what gravity is. Now string theory comes along and says, yes, gravity, quantum mechanics, electromagnetism - all together in one package, but only if the universe has more dimensions than the ones that we see.
— Brian Greene

As you say, the way string theory requires all these extra dimensions and this comes from certain consistency requirements about how string should behave and so on.
Roger Penrose string theory quote

String theory quotes
Picture quote about String theory

In the book, I make the point that here we have string theory and here we have twistor theory and we don't know if either one of them is the right approach to nature.
— Roger Penrose

When we understand string theory, we will know how the universe began. It won't have much effect on how we live, but it is important to understand where we come from and what we can expect to find as we explore.
— Stephen Hawking

Even before string theory, especially as physics developed in the 20th century, it turned out that the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle.
— string theory quotation by Edward Witten