Accounting: Working Capital Changes

how come when you sell inventory, you both recognize that in the SCF through change in NWC (Decrease in inventory) AND you also remove inventory off the balance sheet --

(1)

Ex. assuming Revenue 100 and COGS 50

(I/S) Rev 100, COGS 50, 40% TR, NI up 30 (SCF) NI up 30, Inventory down 50 so cash up 50, cash overall up 80 (B/S) cash up 80, inventory down 50, assets up 30; NI up 30

but then, when you write down an asset (i.e. Bad debt expense) you only reduce the value of the asset A/R on the balance sheet, but you don't recognize it in changes in NWC?

(2)

Ex. assuming Bad debt expense writedown of 50

(I/S) Bad debt expense 50, 40% TR, NI down 30 (SCF) NI down 30, add back noncash writedown expense 50, cash up 20 (B/S) cash up 20, A/R down 50, assets down 30; NI down 30

Like why in 2 is everything balancing without accounting for the change in NWC from the change in A/R from the bad debt expense?