Will quantum computing pave the way for native, true RNGs? Obviously, regular computers can't generate random numbers on their own, since they're inherently systematic machines. Would quantum computing be able to run a true RNG without a seed based off user input (or any other external variables)?
Actually, today's computers can generate truly random data on their own, and many in fact do. The random data is produced as a byproduct of the physics of the components, not as the product of a given algorithm, so it necessarily has to be implemented in hardware. But the hardware is readily available. 

The popular TPM chip, for example, typically has an embedded TRNG, as do many security-oriented peripherals, such as some authentication tokens. 

The actual mechanism used to harvest sources of entropy varies by component, but a simple-to-understand mechanism is the analysis of noise generated at the avalanche breakdown of a P-N junction of a diode or transistor. The noise from such a cascade is actually the amplification of the random movement of electrons at the junction - essentially amplifying the randomness of quantum mechanics to the level where it can be read by traditional electronics.

Obviously this isn't the only mechanism you can use to harvest randomness in today's computers, but it's an easy one to understand. In fact it's worth pointing out that the Intel's recent Ivy Bridge architecture introduced a new instruction: RDRAND, which yields the output of an on-chip TRNG. IEEE Spectrum has a detailed write-up of how it works.