When installing a custom ROM shouldn't we wipe system partition along with data, dalvik, and cache? What are the differences with and without wipe?
You should. That is a "clean flash" and is normally recommended in installation instructions. This ensures that the ROM is written on a clean slate
At times, like in the case of "nightly" ROMs or some mods to ROM,
/system is not wiped but written over the existing system called "dirty flash" (not even
/data or cache is wiped)
As a thumb rule, switching over from stock to custom ROM or from one custom ROM to another, clean flash is recommended. ROM chefs clearly mention this in instructions. Also, if you are upgrading to a higher version of ROM by clean flashing it (Thanks to Izzy who pointed this in comments)