Had Yar lived and remained Security Chief, just as on DS9, Worf could have easily just been the Tactical Officer\Klingon Liaison. Those two positions, especially after Tasha died, were sort of blurred, but they really were two distinct functions: security chief essentially being the "top cop" aboard the Enterprise, and Tactical officer being responsible for ship weapons and shields, and making tactical\battle recommendations.
Now, here is a thought: what if they stuck with the original plan and Crosby was cast as Troi, and Sirtis was cast as Yar? Would Crosby still have left? Would Sirtis been more interesting?
Edit: seeing as today is International Talk like a Pirate Day, henceforth for the rest of the day, let's refer to Tasha as YARRRRRR!!