There are a couple of separate benefits as mentioned above, the obvious one being to make use of all available power. No good having a 100A intake with 120A on one phase and 60A on another.
Next is if there are 3-phase motors on the system and any significant voltage drops, one wants all the drops as close as possible so that the motors see a symmetrical voltage. Suppose a long submain was feeding a board with 3-phase machinery and some heavy single-phase loads. If the single-phase part of the load is unbalanced then so will be the voltage drops on the three lines. Motors in the 3-phase machinery will then try to regenerate power into the lower phase(s) or at least draw less power from it, in an attempt to balance the drops, resulting in increased winding current and heat dissipation.
Finally there is a situation where in large industrial distribution, due to the generally balanced nature of machine loads, the neutrals are significantly reduced to save copper. These systems can only withstand a certain fraction of imbalance before the neutral current is exceeded. E.g. in a production hall with a 600A maximum line current, there might only be 50A of neutral current / imbalance to supply the 230V electronics. DNO's distribution cables sometimes have a reduced neutral as the diverse nature of a load made up of many customers spread across the phases makes for very low neutral current overall.
When systems with reduced neutrals get re-purposed they can come to grief. In 1995 a large feature film production moved into a disused wartime factory complex and connected the lighting distribution panels to the existing submains that had served production machinery. Film and theatre lighting can by nature be heavily unbalanced as any combination of lights might be turned on or off at any one time, and due to the 3n harmonics produced by phase-angle dimming the neutral current can be artificially high. The submains with reduced neutrals soon made themselves known.
I have an interesting story to tell about unbalanced 3-phase entertainment systems loads but this post is long enough already.