To give some light as a former repair tech at an apple store, these "calibration machines" were a required step whenever a display was replaced on any iPhone, though there were two specific types: one for 3D Touch, and one for without (basically, is it an iPhone 6s or newer vs iPhone 6> | iPhone 5/5s/SE). The machines were multi purpose for the repair process, first it verified the phone would boot into a form of iOS or custom software, perform various pressure sensitive touch tests (hence the 3D Touch vs non-3d touch), and then finally, re-assign serial numbers or pairing of Touch ID to the logic board. The biggest problems we ever had with these machines would be service outages (since the software had to communicate with servers to authenticate the display replacement and re-assigning the serial numbers of the display/touch-screen/touch-id to the logic board), or when the machine would refuse to calibrate any phone display, leading to delays and downtime (queue 30 minutes worth of angry customers asking where their phones are when the new display is still waiting in line for the now one and only working calibration machine for that type). All in all though, for what would usually take an at most 20 minute display replacement repair would turn into the full 45 minutes just because the calibration machine would be sitting there doing it's "thing" for 15-18 minutes. Worst yet, if we had to restart because of a dreaded adhesive failure message (the 3D Touch calibration machine would somehow "magically" test for this, no idea how it ever tested or how it was triggered, just thought it was some failure somewhere else), it would mean an additional 30 minutes added... Oh, and don't forget, these machines are vibration sensitive, so "vibration detected" would be an additional 15-18 minutes to redo the calibration... If all goes well, the phone successfully restarts into whatever iOS it entered in with, with no data loss, and a new functioning display! If not... well, as some people already mentioned, a new white box replacement iPhone of the same model and spec was given for the cost of the display.
This change of being only software is a little interesting from this perspective, since it might mean that the technician performing the repair will have to manually perform a touch sensitivity test in place of the calibration machine doing it (anyone in AASP or Apple may recall the touch pad calibration test for MacBook pros with those weights).