Why feature crosses may work better than having them as individual features?
It is not necessarily cross features. Actually, it is a subset of a general concept, namely, kernel trick. Using kernel trick you will be able to find decision boundaries which are more complex than usual hyperplanes which can be found using the linear combination of current feature space. Suppose you have a single feature $x$. By employing that you will be able to make a line as a separator of two classes. If you add $x^2$ alongside $x$ you will be able to have a parabola decision boundary rather than a simple line, which enables you to have a complex decision boundary in cases which is needed. Moreover, because you have both $x$ and $x^2$ you can set the coefficient of each to zero which means you have a kind of flexibility to decide to have a simple line or a parabola.