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Since approval of bad debt write-offs is an accounts receivable authorization function and reconciliation of accounts payable is an accounts payable reconciliation function, there is no incompatibility between the two functions.
Recording of cash receipts is a recordkeeping function and preparation of bank reconciliations is a reconciliation function. If the same person were to perform both functions, that person could misappropriate cash payments and conceal the misappropriation by falsifying the reconciliation.
Even though distribution of payroll checks is a custodial function and approval of sales returns is an authorization function, since the two functions are unrelated, there is no incompatibility between them.
Posting to the general ledger is a recordkeeping function, and the fact that posting is done for both cash receipts and cash payments does not create an incompatibility, since they are different functions.