If one forms an LLC as a holding entity for child C-Corporations, would that allow the C-Corps' access to financing or would investors see the parent LLC and be turned off?
What do you mean by "allow access to financing"? A fair number of founders maintain their stock ownership through an entity like an LLC. This could be for all sorts of reasons (tax planning, separating assets/liability). I would expect a potential investor (or their lawyers) to ask for the reasoning behind the structure, but assuming it's a relatively simple answer, that would be unlikely to have any major effect on the investment decision.
My guess is they would be turned off because control of the LLC could be transferred without their approval and could potential shield the owner of the LLC from litigation by the investors.
They want your personal name on there so they can come after you personally in case something fishy happens.