For the bulk of biologists, though, the most interesting questions are those which relate closely to our own species. It's hard to resist the draw of learning where we came from or potential medical miracles such as stem cell research. We can't really learn much about those kinds of things from plants.
Or can we?
Well, yes and no. Some questions, like learning where we came from, can be answered through methods that apply equally well to humans and pretty much any other species. Population geneticists and genomicists aren't really limited to a particular focal species in their work, because the principles apply across species. Some of the details, such as the difficulty of DNA extraction, the rates of nucleotide sequence divergence, or the suite of possible mating types, may differ a bit. However, determining the relatedness of individuals or populations is going to be pretty much the same no matter what sort of organism is being studied.
The methods derive strongly from mathematics and statistics, so they mainly just need some tuning to fit the organisms of interest. In other words, we could practice on plants to understand population genetics before deciding to roam the countryside telling people around the world where their ancestors came from.
Of course, we could also practice on just about any other taxon instead. There isn't much about plants that says they are the best analogue for studying human population genetics.
Stem cell research might be a different story, though. Plant biologists have actually been dealing with stem cells for about fifty years now, after all -- with immense success. The reversion of plant cells to pluripotent, if not totipotent, callus tissue is actually fairly simple and can be achieved with the proper balance of two plant "hormones" or growth regulators, cytokinin and auxin. Move the callus to a medium (typically an agar plate or liquid suspension) containing a different ratio of the two hormones, and you can regenerate roots, shoots, embryos, or even flowers.
Success does depend somewhat on the source tissue, with embryos and anthers often making the best choices, and some species are more recalcitrant than others. Resolving such difficulties is often a matter of optimizing the growth medium; at the very least, nearly all plants can at least be micropropagated (essentially, cloned from intact tissues such as a piece of root or stem) using these methods.
Plant tissue culture has been highly successful as a form of biotechnology. It has enabled follow-on technologies such as Agrobacterium-mediated and biolistic genetic transformation. It has allowed the mass production of plant clones. While mass production does have the potential to reduce genetic diversity as a whole if used indiscriminately, it also can assist the conservation of rare plants by building up population numbers. Tasty varieties of perennial plants such as raspberries can be propagated virus-free by regenerating apical meristems -- the tiniest new leaves at the tip of the plant -- in aseptic culture.
In addition, the parts of medicinal plants which produce the most phytochemicals can be grown independently of the rest of the plant. Finally, tissue culture provides an interesting experimental system to understand development and morphogenesis. Given a small ball of plant cells, what processes occur in the plant genetically and physiologically under different cytokinin-to-auxin ratios that allow it to regenerate roots as opposed to shoots?
Realistically, plant tissues do not differentiate to the amazing extent that animal tissues do. The control over plant stem cells we have arises partly due to the relatively small number of variables responsible for cellular differentiation. Furthermore, that control is still rather limited -- we can generate roots from callus, for example, but we don't necessarily have the ability to grow only root cortical cells.
A loose analogy for humans might be the ability to regenerate a skeleton, but not specifically bone marrow cells. Nevertheless, plant biologists have been doing for years what scientists studying mammalian cells have been working hard to achieve: the ability to produce major organs or even whole individuals from a single cell.
While the factors at play for organ regeneration in animals and plants certainly differ, it would be interesting to examine genetic similarities in developmental patterns to see if plants' more modular growth and differentiation can help inform research on mammalian stem cells, with their rather deterministic development. Including another taxon with an intermediate regenerative capacity as a third study system would be especially informative. For example, some reptiles can regenerate body parts lost to predators, and others are capable of parthenogenesis. Analagous processes in plants are quite widespread, but in mammals they are unheard of outside the laboratory.
Comparative genomics and systems biology research comparing and contrasting development in a well-understood plant such as tomato (which may have determinate or indeterminate growth depending on the variety), a regenerative reptile like Ophisaurus, and mice could potentially be quite informative. Mammalian stem cell research has come a long way in the past decade, but it never hurts to do a little comparative work using organisms particularly suited to the question at hand.