Kinetic energy from a projectile is equal to the mass of the projectile times the square of the velocity, but air resistance saps velocity off quite rapidly and independently of the mass. So a heavy projectile will deliver more kinetic energy to a target than a lighter one with the same initial velocity.

A lighter projectile can be driven faster by the same charge of propellant, but air resistance increases with the cube of the velocity so delivering more energy through increased velocity is a losing game. You can decrease air resistance by decreasing the cross section of the projectile, but that requires dense materials like lead.

tldr: the difference is absolutely not minuscule. There’s a reason why bullets are made of dense materials.

Of course it isn't an energy multiplier. The energy carried as the bullet leaves the barrel will be very very close to the same. The energy it carries will be lost more quickly to air resistance with a less dense round though. Especially since the same powder behind less mass, means more speed, means more air resistance. How much that matters depends on a lot of factors, but it can certainly be enough to matter.

You're correct, but also completely wrong at the same time. Yes, you can have a lighter bullet that is faster that carries the same kinetic energy. It might even hold its energy longer if it's more aerodynamic. Where you are wrong is the ability to transfer that energy. A full metal jacket would pass clean through the target without transferring most of its energy into the target. A lead bullet that deforms is going to dump a lot more energy into the target. That's why you have hollow points and other bullets that are designed to petal and fragment on impact. For hunting the goal is a bullet that does pass all the way through creating two wounds to bleed out and cutting as large of a wound channel as possible. Which is different than say self defense where you want a bullet that dumps all of its energy as fast as possible so you don't over penetrate and hit your neighbor.

I guess all of that falls in line with the force being concentrated. It just really isn't related to density as much as you're implying. Unless I misunderstood what you're saying.