The point of identifying a primary publisher is to have a single Publisher handler things like sending notifications to users or analytics info to Adobe Analytics (if used).
For example : if you leave all publish instances as primary and a community member sends another community member an inbox notification then when SCD sync's the data between publish instances each publish will send a notification. This isn't really desirable so you assign a single Publish to handle these tasks.
In regards to the implication of disabling this, you should. If you have 4 aem publish instances synchronizing data via sling content distribution you only want a single one of those publishes enabled as primary, the other 3 should have that property unchecked