A switching converter/amplifier is a system with an inductor and capacitor and, thus, is described by a dynamic system with a harmonic oscillation solution. Designers, however, use a simplified, straight line approximations, like (for Boost):
ΔI = (Vin-Vout)/L × ΔTonΔI = Vout/L × ΔToff
The linear approximation is used in calculus for infinitesimal increments. Yet, the system switching time is quite finite. The second thing that bothers is that Vout changes as much as the the current. Why only current delta is accounted?
Because the high-order non-linearities are not involved, ΔT is small enough. The deltas are used when they are small in comparison with the value itself. Therefore, ΔV does not affect the current delta. Actually, it is accounting the deltas that arises the non-linearities.