GaN-based LED's have only been commercially available since 1994, and only recently at a reasonable efficiency and price. Using LED's is quite different from using tungsten filament or gas discharge lamps (aka flourescent lamps).
As mentioned previously in these comments, plants only absorb a small fraction of the solar irradiation. For example, chlorophyll, the dye molecule used by many plants, only absorbs significantly in relatively narrow bands of the blue and red, corresponding to 2% of the total solar irradiant power.
It turns out that the bandwidth of these absorption peaks matches quite closely with the bandwidths of blue and red LED's operating near room temperature. Thus, even with 20% efficient LEDs the total power-to-plant-product efficiency can likely approach 100%. If you replace the plants with standard 18% efficient solar cells, you could feasibly have several layers of plants powered by the same footprint, although at a greatly increased capital cost.
If you add in the improved control over germination and growth afforded by an enclosed and highly-regulated environment, the economics might begin to make sense, especially considering the long lifetime of color-pure LED's (much longer than phosphor-converted LED's).