It is, indirectly, linked to fines.
The main reason for cutting the LA out of the education loop is cost.
Each LA gets allocated an amount of money to pay for the central administration of local authority schools. The more schools that are academise in the area, the less the LA gets.
The budget allocated to schools is based on a complex formula per pupil, and is given directly to Academies. LA schools receive their grant via the LA. Before they give it to schools, the LA cream off an an amount of money (called de-delegation) to cover the cost of certain services to LA schools - things like insurance, H&S services, payroll etc may be included, it varies from LA to LA. It may also include the provision of non-statutory Education Welfare Services, which includes things like late sweeps outside schools etc.
Academies don't have money creamed off their grant by the LA,, but they do have to pay for those services separately. What is becoming apparent is that it is cheaper for schools to buy those services independently than the amount the LA takes from LA schools for them.
And, There are several companies that offer Attendance Services such as late sweeps to schools - and will also administer the issuing of Fixed Penalty Notices etc, which in most LA schools is done by in-house staff given extra hours or overtime.
So Academisation saves the in two ways; it reduces the amount given by the Govenrment to LA for administration, and it creates a competitive market for support services to schools so more money is available in the school budget for education.
So even if Academisation doesn't improve results, as long as it's not detrimental to results, while at the same time being cheaper, it's a good thing, I think?