Theophrastus looked at plants and asked what distinguished one from the other. He saw differences in trees, shrubs, herbs, in roots and leaves, from one plant to the next, and so created the basics of modern taxonomy. Dioscorides looked at plants and asked what they could do for humans. He saw differences in uses, in medical applications and foods, and codified an early version of economic botany.
As fortune would have it, Dioscorides' work thrived from ancient times until the Renaissance. Theophrastus got buried in a pit and mostly forgotten. Plant taxonomy as we know it languished until Europeans regained an interest in the natural world. One big problem? No one knew what to call plants. No one knew if they were talking about the same plant. Local names were handy locally, but worse than useless scientifically. It took Linnaeus and his system of binomial nomenclature to finally make it possible to have a coherent discussion about a particular plant and for all participants to be certain that they were discussing the same thing. (See Anna Pavord's book The Naming of Names for an excellent overview.)
Linnaeus and his descendant taxonomists follow essentially the same rules as Theophrastus. They look at physical features of plants. Plants that share features get grouped together. Genetics and DNA mapping have allowed taxonomists to create groupings that are more evolutionarily accurate than groupings created by mere gross physical resemblance - for example, Sarracenia and Nepenthes are not close relatives even though they are both types of insectivorous pitcher plants - but the principle remains the same, plants grouped on the basis of physical similarity.
All of this means that plant taxonomy is a weird, free-floating subject of study. We memorize identifying features such as placentation, leaf arrangement, number of carpels and ovary placement. We use these traits in dichotomous keys to place plant specimens into families, genera, or species. So, for example, we know that members of the family Salicaceae are trees or shrubs, the lowermost bud scale is centered over the leaf scar, the flowers are reduced, unisexual, and subtended by hairy bracts, and that the fruits are loculicidal capsules. Members of the Fabaceae have root-nodules containing nitrogen-fixing bacteria, alternate leaves that are typically compound, stipules that range from inconspicuous to leaf-like, and usually five sepals.
But what does that tell me? These synapomorphies, or shared features, are the result of evolution, of millions of years of natural selection. The social Hymenoptera, which include bees and ants, appeared during the Cretaceous (145-65 mya). Angiosperms appeared between 130 and 125 million years ago. The Asteraceae appeared around 50 million years ago, during the Cenozoic era. The Cenozoic started 65 million years ago, after the end of the Cretaceous, and after the dinosaurs disappeared. This was the age of mammals, but also of various other kinds of life, especially insects. The Asteraceae thrived and radiated during the unstable climate of the Pleistocene - 2.5 million to 12,000 years ago - downright recent by human standards.
Homo sapiens, on the other hand, appeared about 200,000 years ago, and only got to looking and acting modern 50,000 years ago. What have we to do with plants? They were all here when we arrived on the scene - whatever morphological features they "chose" were not chosen with us in mind. Plants are speaking a very different language from ours, and on a different timescale. They were formed by insects and other animals and climates and geography that we can never know.
This, I think, is why economic botany tends to win out over pure systematics. We teach students economically important plants in each major plant family - peaches come from Rosaceae, cotton from Malvaceae - because otherwise it is awfully difficult to persuade them that they should know the classifications. The plants simply aren't talking to us. We don't assess flowers for landing strips or accessibility for our probosces. A magnolia flower has a lot to say to a beetle and rose perfume says a lot to bees, but to us they're just pretty. The ginkgo still makes fruit that may have been custom-blended by dinosaurs, and the durian makes giant spiny fruits that might have been intended for elephants. (Connie Barlow, The Ghosts of Evolution.) No wonder we focus our study on "useful" plants - otherwise we feel left out of the discussion.
Pure taxonomy - we need the names named, so that we can know what we're talking about. But I find it tantalizing, dancing around real answers. How is it that I can study botany for years and still can barely identify a single insect? Why are we studying plants in splendid isolation, instead of pairing them with their many partners? Why doesn't taxonomy start with a chronology, slotting plants in where they appeared, along with animals and other living organisms and continental positions and climate? (That's a poster I've been planning to make for years. Complicated, it is.)
There is so much more to why plants are what they are than their medical and fiber applications. Applied plant science is all very well, but the full story is so much more interesting. Even if it's still fragmentary, we could be telling it.