In my view it's always better to have more resolution than is sometimes needed than less resolution than is sometimes needed, provided there is no downside to the greater resolution, such as greater noise. More resolution is also great for cropping.
The problem with HD, (that is full HD at 1080p), is that most sources are currently way below that standard.
I have a fairly recent plasma 65" HDTV model. The best video image quality I've seen so far is from a Bluray at 1080p input, and the highest resolution stills are my own, downsampled to 2mp.
Clearly 8mp, or double the resolution, would be a huge improvement, but what is perhaps not clearly understood is that such increase in resolution and detail would be discernible only from a proportionally closer viewing distance.
Having done some experimentation regarding optimum viewing distances from a 65" screen, I've found that in order to see all the detail provided by a good quality image of a mere 2mp (or 6MB), one should not sit further away than 3 metres, or even 2.5 metres.
For the usual crap-quality HDTV transmissions, viewing from a 6 metre distance is better. To appreciate the extra resolution of an 8mp image on a 65" screen, one would have to sit considerably closer than 3 metres, which is neither practical or desirable.
I once had the experience of viewing an opera in the cinema, recorded in HD and projected with equipment which was possibly 4k, but maybe just 2k. The only seats available were near the front row. The image quality was crap. After the intermission, we discovered some spare chairs and took them behind the back row where there was a walkway. From that distance the image quality was perfectly acceptable.
The advantage of a 4k projection of a 4k source, I guess, would be an acceptable image quality from or near the front row of a cinema theatre, or from a seat positioned just 1.5 metres or closer from a 65" TV in one's living room.
To really appreciate that extra resolution from a 4k source in one's home, one would need a 4k digital projector and a 120" screen.