While that's a factor, it's a very minor one - soft metals (lead and copper) are used as projectiles primarily because the bullet itself deforms to engage with the rifling when fired (softer materials also present far less wear on the rifling as a result - this is why shotguns, which are smoothbore and thus far less delicate, often use steel projectiles). For rifles, the weight of the projectile is very secondary to the mechanical properties of the material while it's being fired, and in fact there are many brands of ammunition available that use steel cores jacketed with a softer metal (though almost entirely for their penetrating ability - the deformation of a solid round you get with softer materials is actually far more desirable when hunting since you're less likely to go through the animal you've shot.)