Actually , there are a very few instances where a neutral can be theoretically overloaded . They are in situations where harmonics are created by the loads . Computer equipment ( a lot of computer equipment , like a server farm ) and florescent ( older , I think ) lighting .
But it unlikely you will run into this in a residential environment .
Now , if you loose your neutral , unlikely you will overload the neutral , but all sorts of crazy / bad things happen .
As for as unbalanced voltage , on single phase 120/240 VAC , voltage phase to phase will be what ever it is . Voltage to neutral can be different .
And load affects voltage .
The short answer of why the neutral & earth ground are bonded at the service entrance main disconnecting means , has been answered . It involves having a safe / reliable / low impedance path for the voltage / current to go , to facilitate tripping overload devices .
All in all , balancing load on a home loadcenter is not normally a thing to loose sleep over .
Merry Cghristmas and Happy New Year
God bless
Wyr