There are some examples generally due to the issues with lenses and crop factor plus ergonomics this is not popular choice
What si missing from this discussion for me is the 2k RAW footage from the Blackmagic Pocket Camera. From the samples I have seen I think it looks nicer than 4k. I would love to see some well graded underwater footage from it but can't find any.
I would not agree it looks better than GH4 and even some normal HD either