It may interest you to know that depression and anxiety relate to emotional stability (essentially the opposite of neuroticism), a personality trait which tends to decrease over the lifespan, especially in young adulthood (Roberts & Mroczek, 2008). Here's a figure depicting this trend (bottom left):
This article points out that most of the personality changes depicted above occur during young adulthood. This supports the hypothesis that plasticity is an important enabling factor in these changes. Roberts and Mroczek also describe these changes as mostly positive, which supports the hypothesis that these changes are a partly intentional process of social adjustment. I'm not aware of any evidence that supports these hypotheses more directly, but any such evidence would also support the plausibility of interventions that target neuroticism during earlier life stages when plasticity is generally greater.
The language of plasticity appears sparsely in a similar article that describes change in adult personality (Srivastava, John, Gosling, & Potter, 2003), though no explicit references to neural plasticity appear. However, this article also presents a complication and a challenge through its own evidence of change in neuroticism over the lifespan, depicted in this figure (top left; neuroticism $\approx (-1)\cdot$ emotional stability):
The complication is the sex difference in change over time: only women's neuroticism seems to decrease in this study's evidence. The challenge is the apparent linearity of both trends; neither supports the importance of plasticity. Therefore it's not clear that any intervention focused on altering neuroticism would function equally well for both sexes, nor take advantage of neuroplasticity. Nonetheless, a very recent article recognized the malleability of neuroticism and recommended exploration of options that would intervene at this basic trait level of disorder development (Barlow, Sauer-Zavala, Carl, Bullis, & Ellard, 2013, in press). Thus it seems further evidence to support your idea may be forthcoming!
Neuroticism aside, other recent articles have promoted biofeedback, neural decoding, and neural interface technology as ways of "targeting", "promoting", and "exploiting" neuroplasticity in treating neurological dysfunction (Wang et al., 2010; Seitz, 2013; incidentally, Seitz works at my alma mater and published this shortly after I graduated...it's a small world). Biofeedback and neurofeedback have established applications in the treatment of depression and anxiety (see for review Yucha & Montgomery, 2008). Biofeedback methods seem to have been around just about as long as theories of neuroplasticity (discounting one particularly early study at the end of the 18th century), so I wouldn't say biofeedback was intended as a neuroplasticity-based approach, but evidently it has turned out to be a somewhat inadvertent application of neuroplasticity. Clearly, theorists and clinicians are actively capitalizing on this convenient convergence of neurology and clinical methodology – this trend seems likely to continue.
- Barlow, D. H., Sauer-Zavala, S., Carl, J. R., Bullis, J. R., & Ellard, K. K. (2013, October 14; in press). The nature, diagnosis, and treatment of neuroticism: Back to the future. Clinical Psychological Science, DOI: 10.1177/2167702613505532.
- Roberts, B. W., & Mroczek, D. (2008). Personality trait change in adulthood. Current Directions in Psychological Science, 17(1), 31–35. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2743415/.
- Seitz, A. R. (2013). Cognitive neuroscience: targeting neuroplasticity with neural decoding and biofeedback. Current Biology, 23(5), R210-R212.
- Srivastava, S., John, O. P., Gosling, S. D., & Potter, J. (2003). Development of personality in early and middle adulthood: set like plaster or persistent change? Journal of Personality and Social Psychology, 84(5), 1041–1053. Retrieved from http://j.b5z.net/i/u/2043019/i/PersonalityDevelopmentInAdults.pdf.
- Wang, W., Collinger, J. L., Perez, M. A., Tyler-Kabara, E. C., Cohen, L. G., Birbaumer, N., ... & Weber, D. J. (2010). Neural interface technology for rehabilitation: exploiting and promoting neuroplasticity. Physical Medicine and Rehabilitation Clinics of North America, 21(1), 157–178. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2788507/.
- Yucha, C., & Montgomery, D. (2008). Evidence-based practice in biofeedback and neurofeedback. Wheat Ridge, CO: AAPB. Retrieved from http://web.archive.org/web/20101009135554/http://isnr.org/uploads/EvidenceBasedYuchaMontgomeryW.pdf.