Substrate has three functions: its physical function, its adsorptive surfaces, and its role in biofiltration.
Physical function. First of all the substrate provides a physical anchor for plants in a natural-looking setting. But substrate has physical functions even where there are no plants. Some fish are uneasy in a tank with a bare glass bottom; the shiny surface reflects surface light and their own shadowy movements and makes them skitterish. Light reflected from below disorients them. So, you'll reduce unnecessary stress, even in a temporary quarantine or hospital environment, by providing even the thinnest layer of gravel, just enough to cover the surface (even if you feel you must boil it afterwards).
Adsorptive surfaces. Second, a matured substrate offers sources of nutrients for the plants, mostly in the form of surfaces to which nutrients can adsorb. On the whole, nutrients should not be in the water, but in the lower substrate, beneath an unenriched, well-rinsed capping layer. In the enriched lower layers adsorbed cations lightly cling to ion exchange sites and remain available to plant root hairs.
Different materials in the substrate have varying affinities for adsorbing nutrient cations. Their capacity can be rated by a soil scientist as their Cation Exchange Capacity (CEC). Increasing CEC values can be represented in the sequence: "aquarium" gravel, sand, silt, colloidal clay, peat, humus. If the issue of sufficient plant nutrition in the substrate concerns you right now, perhaps you should also be scoping the nutrient deficiency threads archived at TheKrib.
Biofiltration. The third function of the substrate is to offer a vast range of colonizable surfaces for a diverse community of bacteria some of which are the agents of biofiltration, together with water-filled interstitial spaces of varying scale. The aerobic bacterial communities that metabolize ammonium to nitrite and then to nitrate have been a well-known feature of the substrate since the introduction of the undergravel filter in the 1960s. But sometimes people don't seem to realize that for every free-floating bacterium in the water column, there are hundreds of thousands settled in the biofilm, efficiently metabolizing one another's waste products. And on a somewhat larger scale, in the various watery environments within the sand and gravel, some of which are quite poor in oxygen, there is also an unexpectedly rich and various community of microscopic meiofauna, which scientists and aquarists are just becoming generally aware of, which also forms part of the biofilm, or benthos.
Though small-scale gravel has more surface area, weight for weight, than coarser gravel, the difference between grades of gravels is a minor consideration when both are compared to the surfaces of flocs of humus. It's like comparing the surfaces of a baseball versus a softball to those in bath sponges of the same diameters. Substrates with a higher CEC rating are also more hospitable for bacteria and the build-up of a healthy biofilm. Such substrates would include silt and colloidal clay, Sphagnum peat and unenriched compost or humus. When these materials are incorporated into the lower layer of substrate in a newly set-up planted tank, they will compensate during the first six months for the initial lack of organic humus. It's silt and floc that keep bacterial populations high, some of the very material, incidentally, that obsessive gravel vacuumers are removing. Bacteria in sand filters of established aquaria, whether marine or freshwater, number about 10 million per gram, which initially sounds promising, but Diana Walstad points out (The Ecology of the Planted Aquarium, p.125) that lake sediments have been shown to contain a billion bacteria per gram.