My position is that it is morally wrong to run a business, at any time, such that ALL creditors cannot be cleared.
Not just immoral; illegal. As you said, trading whilst insolvent i.e. liabilities greater than total assets, can leave the directors liable (although very difficult to enforce due to the company being a separate legal entity and proof is required that the directors were acting in the full knowledge that the debts couldn't be repaid) and be grounds for any creditor(s) to apply to the courts for a compulsory winding-up order.
Cheers
Whirls