I'm not having trouble understanding the concept. What I'm having trouble with is why you keep suggesting it.
Food photography is very rarely shot with lighting from below the subject. The only possible application would be used for shooting translucent foods and liquids where you need light shining through them to show off the delicate nature of the subject matter. Like this:
But even that wasn't shot on a light-table, light-box or whatever you want to call this system you've come up with for shooting food.
Ask yourself why you would even use a system of lighting from below your subject matter. Most food photographs are taken on a solid surface covered in some form of material and the food is usually presented on a plate or some other suitable object. As robbie has already said; how do you get light to shine through a plate? The answer is you don't. Because there's simply no need to.
All the best food photography is shot using a key light and a fill light, positioned above the level of the surface you are shooting on. Most photographers will want to use natural light where possible and simply use a large light source such as a window as their key and bounce back the light for their fill using a variety of reflectors. Should artificial lighting be employed the basic premise is the same, albeit you have the choice of lighting sources to pick from. And with both natural and artificial light you've got to think about the size of the light source, the direction and the intensity.
In a lot of situations you'll need to add a soft light source from above. Unless you're fortunate enough to have a skylight directly above your studio you're going to need to use an artificial light source and some sort of diffusion or bounce light from the ceiling. Whatever you do the effect is the same - soft, even, controlled lighting from above. Not every shot calls for it but it's very useful to have the option.
The single most important thing in food photography is to get a two-dimensional medium looking as three dimensional as possible. Your theory of 'lighting from below' and using 'cross lighting' to ensure the absence of shadows would be the perfect way of ensuring that never happened.