There are some advantages to casting magic spells over using physical attacks.
Against more agile enemies, physical attacks can prove to be somewhat erratic. This is because there is a form of hit detection used in the game where if an enemy goes outside of the 'hit area' when the attack is executed, that attack will miss. However, magic spells will always hit their target. Magic spells come in two types: immediate impact (such as the Ravager's Ice and Lightning elemental spells as well as most Saboteur spells) and tracking projectiles (such as Ruin, as well as Fire and Wind spells).
Notice that it also takes time for a character that is using physical attacks to literally run up to or chase an enemy before the fighting actually begins. Characters using magic don't have to run or chase after their enemies and their spells tend to reach their targets faster than a physical attack that's being forced to reach the enemy by foot.
Also, the animation speed for a magic attack tends to be faster than the animation speed of a physical attack.
While Strength is only used to calculate the amount of damage inflicted, Magic affects other variables such as the healing power of a Medic and the duration of a Synergist's buffs. This can make boosting Magic stats more useful in general across the different roles.
However, this doesn't mean that physical attacks are worse than Magic ones. Physical attacks have a higher damage multiplier, and therefore cause more damage than spells do. They also have higher Cut and Keep values, giving them higher priority in the heat of battle. And the majority of the most powerful offensive abilities are physical attacks, such as Noel's Meteor Javelin or the Feral Links used by many of the strongest Commando monsters.