Any firm that asked too many questions would get fired and replaced with a more compliant one
Interesting assumption. I have seen many private firms get seriously qualified reports from their auditors, including one that essentially said they couldn't confirm any of the figures in the accounts at all. In some cases the company concerned have stayed with the same auditors.
When I have been involved with audits of private companies I have always found the auditors to be fiercely protective of their independence and determined to ask all the questions they needed. The accountants I know who work as auditors are universally of the view that preserving their own reputation for independence is more important than keeping the business of any one client. Maybe my experience is unusual but I don't think so.
Auditors won't, necessarily detect fraud but they should flag up any inconsistencies between the accounts and the records, failure to disclose matters required by law, etc.
For academies the auditor is required to produce a statement for the EFA covering regularity, propriety and compliance.
None of this guarantees that fraud will be detected. I remain of the view that all forms of organisation are vulnerable to fraud. I have seen nothing to make me believe that any particular form of governance is less vulnerable than others.