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The full color digital printing presses have come to the point that full and four color printing is now possible (but not very cost effective in multiple page formats). Digital book covers have been printed successfully for quite some time. The $1/cover is very cost effective compared to a $750+ makeready on an offset printing press.
The problem comes when printing text. That same $1 applies except for say a 32-page children's book. You essentially have the equivalent of 9 covers or $9 unit cost. This is fine for advance copies or digital book proofs but far too expensive for production copies.
*It is better to look for traditional book printers and binders when you are working on a tight budget.