So much confusion.
macOS creates a so called factory profile for third party displays which is based on some basic colorimetry data found in most modern display's EDID. This profile can be safely deleted (it will be recreated when the display is next connected). This profile is technically lost when the Mac is reset, but it obviously does not matter.
The display's factory calibration (I mean the panel specific calibration done in the factory) resides in a display's firmware (in the form of look-up tables which the display uses to figure out how to translate the input signal to the panel using its display specific EOTF formula) and is meant to correct panel specific deviations so the display produces the proper colors with some reference input and (if possible) in a multi-monitor setup the same display model (from a close batch) look the same next to each other - this usually ensures that the display generally has an acceptable output with the factory calibration. Some displays also have reference modes (like sRGB, Adobe RGB etc) which should make colors right when a corresponding pre-installed profile is selected in the OS. The quality of the factory calibration varies. All this won't be affected by a Mac reset/reinstall. The factory calibration and the factory profile created in macOS based on the EDID should not be confused, they are two different things.
There is then custom calibration and profiling. Profiling means that we set the display to some baseline mode and then using a hardware calibrator tool we measure the display's actual optical output to the various color signals we send using the computer and then build a color profile (which describes what is the optical result to various electrical input signals) based on that. This custom profile is meant to help the computer figure out more precisely how to produce the desired optical result (envisioned by the content creator) by sending the right signals to the display. Some displays have built-in options to fine-tune the calibration at display side (even most entry level displays have some kind of color, gamma, contrast etc controls) and some professional displays can be as or even more nuanced about it than what a computer can do with a profile (in this case instead of messing with a custom profile the calibration can be done entirely at the display side - this simplifies deployment as a single reference profile can be used on the computer). Then of course the combination of both can be done at the same time (correcting some things at the display side, other things at the computer side, but this can result in confusion). The custom profiles stored on the computer will be lost with a reset and might require painstaking work to recreate it so it is a good idea to back these up. Custom calibration at the display side will not be lost (until one resets the display itself).
Hope this helps (or maybe it creates more confusion

).