This does not sound practical. In order to etch completely the copper must be completely removed before the etchant is consumed. This means that there will be active high speed etchant on the board after the process is complete without any protection for remaining bare copper.
I have never seen a printer that did not soil itself so I would expect short printer life unless a special printer designed for this process was used.

Finaly how do you get the board from the printer into the stop etching and remove the waste process without spillage or skin contamination? I am not sure I would want to be close to such a powerfull etchant

If it worked and was reasonably priced it would be very interesting but I would prefer a flatbed plotter type of design using one edge / corner registration that would use the same edge and the other corner on the bed to register for the second side on double sided pcb's thus allowing at least 2 side pcbs without vias to be "home" produced. We all know that via's are never a problem :) but they sure multiply on multi level boards.
Terry