But you don't need a academy programme to allow schools to determine their own curriculum
I agree. However, many LAs have historically used control of community schools to restrict the school's autonomy in this regard.
I believe that every parent should be able to choose their local school safe in the knowledge that it is well run and gets good results for its kids
I believe that too. Sadly LA control has failed to deliver that. LA control has delivered a system where parental income is the best predictor of GCSE results. Where the most disadvantaged children get the worst schools. This must change.
Why are they allowed to not publish full details of what they spend taxpayer money on when LEA schools still have to?
Because they are not public sector organisations. They are in effect contractors supplying services to the government (although the treasury has, somewhat perversely, insisted on imposing some controls as if they were public sector organisations). Other contractors providing services to government also are not required to publish full details of how they spend their income even if it is entirely derived from the taxpayer.
Why are they allowed to produce consolidated accounts that hide the spend per pupil per school?
Every set of academy accounts I have seen either states the spend per pupil per school or gives you enough information to derive it. However academies do not have to submit CFR data so it doesn't appear in the performance tables. And I accept that there may be some sets of academy accounts that do not give this information. Again, this is because they are not public sector organisations.
They have no resources to oversee anything
Really? Perhaps you should tell them that. They investigated 1,972 operational compliance cases in 2013/14. And of course academies are also overseen by the EFA and Ofsted. If criminal offences are committed the police can get involved.
I have never (despite your repeated statements to the contrary) claimed that the oversight is perfect. There is no known system for preventing fraud. It happens in all types of school.