People cannot respect or care for what they have never been taught to take seriously or understand. The schools should teach botany from a young age, and teach children how to draw and paint what they see. Then maybe even PBS would start having some serious programs about plants, not just animals. I am also a gardener. As you can see, my perspective is one of an amateur and layperson.
Many gardeners are somewhat hostile to botanists.
They find keys intimidating. I have no problem with common names for truly common plants. Tasha Tudor is perfectly free to call her violas whatever she likes, just as I am free to call my dogs all sorts of weird names. The problem comes when I start asking everyone I know to learn all that stuff, put it in books, rewrite things, and remember that I don't call my dog a dog, I call him a teddy bear. Long live botany, botanists, and scientific names.