Are there benefits to learning to write with your non-dominant hand?
Yes, there are benefits, but I don't think it requires long-term switches.  Studies have used this as a manipulation to try and increase self control and have found that it decrease aggression.  Based on this, once one has mastered using the non-dominant hand, it seems like the benefit of continuing to use that hand might be over (as it no longer requires effort).

See: Denson, T. F., Capper, M. M., Oaten, M., Friese, M., &amp; Schofield, T. P. (2011). Self-control training decreases aggression in response to provocation in aggressive individuals. Journal of Research in Personality, 45(2), 252–256. doi:10.1016/j.jrp.2011.02.001