A few reasons
First, most of the orbs are subject to energy resistance. Arcane Fire, despite its name, is not. (Granted, this does not apply to Orb of Force.)
Second, there is a matter of range. The Orb spells are Close range. Arcane Fire has a much longer range (between the range of Medium and Long).
Third, Arcane Fire can be used spontaneously. Wizards can dump any spell for another attack, if they find it necessary. This is even somewhat useful for Sorcerers, too, since the empowered orb spell would be a full-round action to cast.
Fourth, as a Supernatural ability, Arcane Fire is not subject to counterspelling or attacks of opportunity (though making the ranged attack may be, but then the orb spells would also be subject to that same AoO). The orb spell, despite being empowered to 6th effective level, is actually a fourth level spell, and subject to exclusion by Globe of Invulnerability.
Last (and my personal favorite), you can use Arcane Fire with any spell level. You are right in that a straight comparison with a 6th effective-level spell vs. a 9th level spell dropped into Arcane Fire is not entirely favorable. However, it is nice to do 5d6 with a cantrip (spell level is zero, archmage level is 5: 0d6+5d6=5d6).