I'm not sure why the Tories think that Primary Schools will be leaping at the opportunity to become academies (or something akin to them). Governors, teachers and parents do indeed complain from time to time about lack of freedom in Schools. Some of this is directed to overbearing and controlling LAs who have't quite managed to cope with the idea they can't run Schools the way they used to....
However in an Acadamy things are different, control passes to:
(a) Some kind of partner group who might well be a commerical company, and
(b) Central Government
So much for being able to control their own affairs, an Academy cannot even change its admissions arrangements without the permission of the Secretary of State.
Personally I'd rather take my chances with the Local Authority, at least you have some chance of influence there. A Primary School wanting more local control could already become a Foundation School just with a majority vote of its Governing body. Few have chosen to. Governors in a small primary School already have wide ranging powers which of course in reality means a lot of work and responsibility! They set the budget, hire and fire staff including appointing the Head, deal with appeals from excluded pupils, manage building work etc etc
I don't think that the Tories are being honest. They don't want to allow Schools to be truly locally managed and governed. They just want to replace local authority control with direct rule from Westminster.