That’s a part of it, but we also have to keep in mind that – in medieval warfare – leading from the front was also a big morale boost for the troops. It showed that your commander was invested in the fight, it made running away both an abstract and a personal act of betrayal, and it demonstrated the bravery and chivalry of your king and thus his right to rule.
Robb’s historical counterpart, Edward IV of York, was famous for leading from the front and being universally successful in so doing. Starting from the Battle of Mortimer’s Cross, where his speech to the Yorkists interpreting a terrifying astrological phenomenon as a sign that God was on the side of York prevented a rout, to the Battle of Towton, where Edward intervened to ensure a vital river crossing and then personally held together the left wing which was being attacked from the front and flanks at the same time, to Barnet, where Edward personally held the center against repeated attacks from the high ground and sent in a decisive attack with his reserves that broke the Lancastrian line, to Tewksbury, where Edward’s center fought virtually alone, cut off from his right and left by the hedges, Edward leading from the front brought victory every time.
So I think GRRM decided to borrow from the Wars of the Roses to depict Robb as a brilliant field commander who was never defeated when in command.