Absent Congress appropriating funds specifically for it, yes.
Should Congress do that? That's a separate issue, which is not the court’s job to address.
> He and other taxpayers paid for the studies,
Citizenship, not taxpaying, is relevant for public data, but citizens (through their representatives) didn't choose to pay for the segregation of public and nonpublic information for release on a schedule more expedited than general FOIA releases.
> Document creation should be in the open from the start.
Maybe, though for processes that can involve mixtures of personal private info, confidential commercial info, trade secrets, and public data that will significantly increase the upfront cost of operations.
But neither the executive branch alone nor the courts are the venue for that.