We can, to an extent, simulate a full spectrum through additive and subtractive colour mixing of "primaries", but it is only a simulation. (And Edwin Land demonstrated that we don't actually need all three of R, G and B in order to create the illusion of a full-colour picture with only a comparatively tiny gamut loss. It is a fragile thing, though, and requires the integrative function and cognitive mapping of our brains.
Similarly, we can easily tell the difference between full-spectrum lighting and discontinuous spectrum lighting. Discontinuous spectrum lighting makes us uncomfortable. None of the colours looks quite right. Food is unappetizing, pictures and people less attractive. Did the light-makers just miss the right mix of frequencies by a hair? No -- any scheme that relies on a small number of discreet wwavelengths will cause a similar discomfort. We may not know why we feels the way we feel at the time, but we sho' 'nuff knows we'se feelin' it.
Three years ago I built LED lamp out of some no-name high-power white LEDs (~1€/piece) and last year I got Phillips LivingColors lamp and subjectively I find the light given by bunch of no-name white LEDs more pleasant.