An April 2017 paper might lead to work that gives clues as to whether dreaming has a function.
F.Siclari et al. (2017). The neural correlates of dreaming. Nature Neuroscience, Nature Neuroscience, 20, 872–878 doi:10.1038/nn.4545.
https://www.nature.com/neuro/journal/v20/n6/abs/nn.4545.html

Francesca Siclari and colleagues woke participants hundreds of times in the sleep lab and asked each time whether they were having a Dream Experience (DE), Dream Experience Without Recall of a dream (DEWR), or No Experience (NE).

They found that Brain activity associated with Dream Experience (DE), as compared to NE (No Experience), had reduced power in the 1–4-Hz band in a parieto-occipital region, that is lower amount of slow waves, which are associated with non-REM sleep.  DE with recall of content, compared to DEWR (Dream Experience Without Recall) and NE, was associated with higher high-frequency power (more wakelike EEG) in medial and lateral frontoparietal areas.

So dreaming occurs in NREM sleep because the 'hot spot' is activated.
The next step would be to find out why the hot spot / dreaming, is turned on during sleep, and indeed during REM and non-REM sleep. We could ask the question, is virtual simulation of the world (i.e., dreaming) sometimes needed to complete/enhance memory processing that is occurring during sleep? Does the brain do some memory processing and then need to run a dream simulation to complete the processing?

Also, if we can find out why the 'hot spot' changes during sleep, with deep slow waves decreasing and fast waves increasing, that might give clues as to any function of this physiological change, and any function of the dreams that are then created.

The beneficial effects of discussing dreams are described in the following two papers:
http://journal.frontiersin.org/article/10.3389/fpsyg.2013.00979/full

and
http://journal.frontiersin.org/article/10.3389/fpsyg.2015.00831/full

In these studies dreams were discussed for about 40 minutes and the discussions resulted in high levels of insight about the memory sources of the dream and/or insight about the dreamer's waking life.

​In soon to be published work we are comparing outcomes of such discussions of dreams to discussions of daydreams. Many thanks to the Bial Foundation for funding that work. The results and background rationale for the study were presented at a public event at the Freud Museum, London, on 20th March 2016.

​In all this work the outcomes of considering dreams were assessed just after the discussions.
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One of the aims of DreamsID is to investigate whether the consideration of a dream and of an artwork based on the dream, has beneficial personal outcomes across many months after the artwork is produced.   

   

In our recent as yet unpublished work at Swansea Sleep Lab we have woken sleepers in the lab and asked them for dream reports from REM and deep Slow Wave Sleep. They had kept a 10 day diary before coming to the lab. We later asked them to identify items in the diaries that matched the dream content. We found that items that were incorporated into dreams were more emotional than items that were not incorporated.

​Ernest Hartmann wrote in his book The Nature and Functions of Dreaming (OUP, 2011) that we can dream of waking life emotional events either directly or metaphorically.       

This has now been shown by the following experiment.

In Davidson and Lynch a high impact film of the events of 9/11 and a non-emotional educational film were shown to participants. The critical waking life event was thus experimentally determined, to control for post hoc confabulations between dream content and prior events. There were more literal, closely associated and distantly associated (i.e., non-literal) references to 9/11 after the 9/11 video than after the education video, but the most significant difference was in distantly associated references. There was more fear, sadness, and shock, and less joy, contentment and excitement in dreams after seeing the 9/11 film than after the education film. This suggests dream content has literal and associative or metaphoric content.
Davidson, J., & Lynch, S. (2012). Thematic, literal and associative dream imagery following a high-impact event. Dreaming, 22, 58-69. http://dx.doi.org/10.1037/a0026273