Most decent printers already do this, except for material constraints. You cannot print the electro-mechanic parts, and things like rods and belts can be printed but have sub-par performance that will lead to lesser precision (inadequate rigidity or flexibility).

But yeah, a fair share of my 3d printer was printed by its same model. And this indeed is why good 3d printers like the Prusas, Mendels, etc are getting cheaper (this and cheaper filament prices). These are printers that provide good precision and use parts that are mostly cheap to produce or directly printable by a similar printer.