Why is molality per mass solvent rather than per mass of solution?
Molality $b$ is defined its way because being proportional for the given solvent to the solute/solvent molecular ratio.

Molarity or molar/mass fractions or molar_amount/solution_mass are not proportional to it. 

The boiling and melting point shifts are proportional via ebullioscopic/kryoscopic solvent constants to molality.

$$\Delta T_\mathrm{b}=K_\mathrm{e} \cdot b$$

$$\Delta T_\mathrm{m}=K_\mathrm{k} \cdot b$$



The number of solvent (s) molecules per 1 solute molecules 

$$\frac{n_\mathrm{s}}{n}=\frac{m_\mathrm{s}}{M_\mathrm{s}\cdot n}=\frac 1{ M_\mathrm{s}\cdot b}$$

If we provide as the input the solute mass and solvent volume and density, the above molecule ratio is 

$$\frac{n_\mathrm{s}}{n}= \frac{m_\mathrm{s}\cdot M}{M_\mathrm{s}\cdot V \cdot \rho}$$