Local foods are, as I understand it, supposed to be some combination of more eco-friendly and supporting local farmers.
Growing a potato in your kitchen cupboard using hydroponics and PV+LED is very local, but you'd have to grow a lot of them before you saved more on transport and processing emissions than created by the equipment; and you certainly aren't helping local farmers by doing it yourself.
Why do you support local farmers? Like on a deep level? Deeper than "well they're my neighbors" Why do you support your neighbor over some guy in Nebraska? Probably because his culture an interests align with yours whereas the same is not necessarily true about the guy thousands of miles away and all the parties between you and him. You'd rather be slightly less dependent on the long supply chain than the short one.