What is the most physically accurate representation of color possible in computer graphics? I am looking for theoretical and implemented models to represent color in software that strives for physical accuracy.

I know that "color only exists in the mind" and that it sort of does not make sense to look for "physical accuracy", but still, how much better is spectrum sampling or other more elaborate representations of color to simple RGB, and what benefits will it bring? What drawback beside performance will it incur (or is performance a drawback)?
The most physically accurate way would be to have a $l(\theta)$ which for each possible color frequency has a certain value.

Converting to RGB would then need a frequency responce function for each channel and the result is then $\int_{infrared}^{ultraviolet} l(\theta)F_{red}(\theta)d\theta$.

Reflected light then has a 2 dimensional response function: $L_{reflected}(\theta) = \int l_{incoming}(\phi)R(\phi,\theta)d\phi$. (ignoring the BRDF here for simplicity)

Drawbacks are that instead of just 3 color channels you now have infinite channels to worry about.