Diversity and functional profiling are different things, different approaches. You can study diversity amplifying specific genes. However, to study fuction is important analyze the potential through metagenomics or expression with metatranscriptomics. A shotgun library could help..
Yes it is, phylogenetic diversity (I prefer genetic diversity) can be studied by sequencing few individuals (many studies even consider only one) per population or strain, functional diversity, in addition to that, depends also on growth conditions and age of the organism, so you have to multiply by the number of possible growth parameters at different ages and for multicellular organisms it depends also on the organ, stage of development ...
With current "next generation" or "deep sequencing" technology it is now possible to take a complex sample such as a stool or gut sample with millions of bacteria in it, or a liter of sea water with hundreds of plankton and thousands of bacteria in it, and ask "how many species" are there, or "how many biochemical pathways" are there. To find out how many species, we can pick one gene such as the 16S rRNA gene and target that for sequencing. To ask how many biochemical pathways we do random shotgun sequencing of messenger RNA, and ask how many of the sequences seem to encode proteases, how many look like sugar metabolyzing enzymes, etc.
It is not so easy to go in both directions at once and completely assemble the genomes of each organism in the sample. But anyway, to tell how many species are present we really only need to sequence one gene per cell in the sample (16S rRNA or maybe a DNA polymerase or other "housekeeping gene") while to look at the biochemical pathways present we need to sequence all of the hundreds of messenger RNAs being produced in each cell in the sample.