It is understood that by design custom fields that are specific to an Issue Type will only be exported if that Issue Type is explicitly selected in a query.

However, if the option Any is selected for Issue Type, this should include all custom fields associated with any Issue Type available in the current context (e.g., Project, etc). Selecting Any is an implicit selection of all individual Issue Types, and thus an export of All fields should export all fields, including Issue Type custom fields.