Should insurance write-offs due to untimely filing be included in management reports as bad debt?

There's no rule per se, but write-offs due to time-of-filing are normally included as bad debt. For example, the Medical Group Management Association includes the following in its definition for bad debt:

Losses on settlements for less than the billed amount.

Accounts written off as not collectible (this includes timely filing denials).

Accounts assigned to collection agencies.

In the case of accrual accounting, the provision for bad debts.