Assumptions made in calculating melting point from thermodynamic data
In real life the melting point is determined by measuring the temperature. The entropy of fusion is usually determined by dividing the enthalpy of fusion by the melting temperature.

$$\Delta S_f = \Delta H_f / T_f$$

Your text book calculation just solves this equation for $T_f$ to recover the temperature that probably had been measured before.

Note that for constant pressure the temperature is constant $T_f$ as long as the phase transition takes place.