Why is a rectangular wing with winglets not better than an elliptical wing?
If using Prandtl's lifting line theory, then mathematically/analytically, ignoring issues of wing weight that lead to bell shaped lift distributions and other sorts of intrusions of reality (e.g., stall behavior) the elliptical wing with the elliptical lift distribution is optimal for minimizing induced drag given a fixed wing area.

You can get an elliptical distribution of lift from a rectangular wing via twist, winglets, or other mechanisms, but it will only be elliptical at one cL value. At other values, it will not be elliptical, and thus suboptimal.