Construction equipment serves three uses:
- As you note it can function as a factory that requires no population.
- It can fortify other ground units more than they can self-fortify, making it important to have at key defensive positions.
- It is used to exploit alien ruins after the Xenoarcheology formations have studied them.
Geosurvey Equipment is used to conduct an additional ground survey on particular bodies already surveyed by your survey ships, which are relatively uncommon. The body will be marked as having ground survey potential, and a ground survey can reveal the presence of additional mineral deposits and/or raise accessibilities of existing mineral deposits. As these are fairly uncommon you don't need too many of these formations.
Xenoarcheology Equipment is used to study alien ruins, once this process is completed the ruins can be exploited by construction equipment.
All of these gain additional speed from having more units with the capability in a formation, strictly speaking you
could play the entire game with just one CON, GEO, and XEN element apiece but they would do their jobs very slowly so a few dedicated formations are preferable to get work done in a timely manner. Note that none of these units need supplies as these are only drawn by combat elements, so formations of only CON/GEO/XEN plus an HQ if you want to assign a commander are all that you need.