Would you accept a CIO / CDO job that does not report to the CEO? Why you would? Why you would not?

I'd consider it, but the more likely path to success and job satisfaction would be with a direct report to the CEO. COO's and CFO's care about operations and finance, not aligning technology with business strategy.

Ideally CDO roles would report direct to CEO but in large organisations its common to have a more federated structure where divisions are larger than most companies. This results in multiple CDO (or CDO type roles) so i can see alternative models to CEO reporting lines.  Its more about ability to influence, improve data and run a strategy to me.

I'd dare to suggest that the C Level technology roles need to be revisited - at least in a discussion. 

I would argue the case for a role into the CEO that is more of a hybrid Technology/Business role that is representing more of a broader view (CISO / CDO / CTO / Business) - CIO+? 

I would agree reporting into CFO as example, which was more of a legacy model, is not always ideal - and it does depend on the company size/context - so if the question is if the 'technology organisation' should be aligned to the CEO I would say 'yes', but we need now to look more broadly across RUN, INVEST, TRANSFORM for the right individual and role with the authority to represent all facets of the organisation from a technology and business perspective. 

I would not accept that job as direct access to the CEO is crucial for aligning IT and digital strategy with overall business goals and ensuring strategic influence within the company.