It's not just curve fitting because basis functions have characteristics which make them desirable for the kind of decomposition one is trying to find. We typically assume in factor analysis that factors are gaussian random variables without clear and repeating patterns. Fourrier transforms force us to think in similar terms but accounting for specific dynamics factor (I. E. Basis functions) should capture.
Also how do we construct those orthogonal basis functions for any downstream task is an interesting research question!
Also how do we construct those orthogonal basis functions for any downstream task is an interesting research question!