Why the length constant of passive current flow isn't depend on the membrane capacitance?
Length constants are defined in the 'steady state' regime of constant voltage; capacitance is important for time-dependent electrical functions but disappears in the steady state.

In a real neuron, where you have other time-dependent (dynamic) features like ion channel opening, time constants and length constants interact to determine how current flows in a length of neurite, as you intuit, but these passive properties by themselves are insufficient to describe that behavior: you need to also consider ion channel gating and conductances.

See also https://en.wikipedia.org/wiki/Cable_theory - note how the capacitance is always multiplied by a changing voltage dV/dt in the differential equations.