Bad and Doubtful Debts in the Statement of Cash Flows

Hi there, I hope you're well. I have a couple of queries about how exactly we treat bad and doubtful debts, using the indirect method in calculating working capital for operating activities. The problem I have is, if we incorporate bad and doubtful debts into the receivables balance, then compare receivables with the prior year, we will be misled into believing that receivables have been settled and cash received, and thus to rectify this, we would need to keep the non-cash expense of bad and doubtful debts recorded in the income statement to reverse this. For example, if in 2021 I had receivables of £500,000 with bad debts of £10,000 and allowance for receivables of £50,000, then we are left with an end balance of £440,000 - assuming the prior years balance of receivables was £500,000 too, we will be misled into thinking that £60,000 receivables had been settled, and to mitigate this would have to retain the non-cash expense of bad debts and allowance for trade receivables of £10,000 and £50,000 respectively, so that in the cash flows from operating activities this £60,000 working capital will be deducted by a negative balance of £60,000. Is this the correct approach in dealing with bad and doubtful debts in the statement of cash flows? I only ask as it seems counterintuitive to deal with the issue by acknowledging a non-cash expense, when the idea of the statement is to remove all non-cash items. Thanks.