Why not estimate coarse albedo from coarse brightness (B_u) directly?

[howardchina]

If I get the optimised $L_c$ from Equation 3, then the aggregated shading map is very close to $2 B_u$.
Then watching Equation 4, why not just represent coarse albedo from $B_u$ ?
$$\tilde{A}=I_u (2 B_u)^{-1} $$