bioware wants you to play the game more, forcing you to have characters on both sides encourages that. Its maybe also part of a plan to balance out the faction imbalance a bit.
If you're asking why your characters would interact with each other, well thats completely up to you and your RP, my 3 main characters are brothers, seperated at birth, on given to the sith (warrior), one to the jedi (knight) and one to slavery (inquisitor). of course they will help each other to get that fancy assassin droid.
you might call that arbitrary, but this an RPG, even an MMORPG where you are supposed to build your characters on your own by a fair amount. SWTOR with its many choices especially encourages players to do exacly that. you are supposed to find your own reasons for your characters to work together. apart from that, the republic and empire do work together on many occasions in the game. battle for ilum for instance or I just did the hoth quests with my knight where you take down the gang leader with imperial troops. it may be uncommon, but there are several examples.