Nanopatterned FePt nanodots often exhibit low coercivity and a broad switching field distribution, which could arise due to edge damage during the patterning process causing a reduction in the $L{1}_0$ ordering required for a high magnetocrystalline anisotropy. Using an atomistic spin model, we study the magnetization reversal behavior of $L{1}_0$ FePt nanodots with soft magnetic edges. We show that reversal is initiated by nucleation for the whole range of edge widths studied. For narrow soft edges the individual nucleation events dominate reversal; for wider edges, multiple nucleation at the edge creates a circular domain wall at the interface which precedes complete reversal. Our simulations compare well with available analytical theories. The increased edge width further reduces and saturates the required nucleation field. The nucleation field and the activation volume manipulate the thermally induced switching field distribution. By control of the properties of dot edges using proper patterning methods, it should be possible to realize exchange spring bit-patterned media without additional soft layers.