Do rail gun systems require high voltage?
I'm curious why many designs would have high voltage ratings, when the objective is to have high current


That's true, the force exerted on the projectile only depends on current, not voltage.

But... we want the current to go from zero to "a lot" very quickly. If the current ramps up too slowly then the projectile will not get full acceleration at the beginning. Optimum current delivery should expend all the energy in the caps and transfer as much energy as possible to the projectile. Any energy left in the caps at the end of the shot is essentially wasted. 

I have no idea what the optimum current profile is. If rail melting is an issue, it would make sense to use lower current at the beginning and increase current as the projectile picks up speed, as higher speed would spread the heat over more rail area.

However... we're going to have a huge current step, which means huge di/dt, and this means inductance is an issue:

\$ \frac{di}{dt} = \frac{E}{L} \$

Let's consider the circuit, this is going to be a "wet finger in the wind" level of precision... Inductance of the capacitor bank and wiring... something like a 5m x 50cm square loop... 5µH. Okay, let's round this up to 10µH.

The US Navy's railgun shoots at about 2km/s, with a 10m barrel this means acceleration time should be 10ms. We'd like the current to ramp up much quicker than that, say 100µs.

With 1000V, di/dt = E/L = 100M A/s, and over 100µs this reaches 10kA.

You can input any number you like into this calculation, especially if you manage to find the real numbers from a real railgun... but IMO the main reason to have high voltage is going to be the need for very high di/dt versus inductance.