Now these sites are really screaming to be a WHS. The dzongs of Bhutan are iconic buildings, they are of critical importance for the history of Bhutan, they are a blueprint for the whole bhutanese architecture and they are also just really beautiful buildings ! They are impressive from the outside, all with quite picturesque locations, and they are impressive from the inside, as they are full of decorated courtyards and colorful temples. And all are still actively used as religious and administrative centers, with wonderful festivals inside of them. Now that's how to be a worthy WHS site, you hunting grounds and vineyards !
I visited three of the Dzongs, had a look at the forth and didn't found out much about the fifth. Here are my thoughts on the individual locations:

• Paro Dzong (The close one): You will probably see this one even before touchdown, as it is quite close to the only international airport of Bhutan. It is probably the one which resembles a castle the most: There is a keep in the middle, a strong ring of walls, a moat and guarded entrance doors. It doesn't have as many courtyards as the other Dzongs, but is still a very fine building, with lots of wooden decorations and towering walls. You shouldn't feel too bad if this is the only Dzong you can visit, as it's a good example of the dzong style.
• Punakha Dzong (The beautiful one): This one is advertised as the most beautiful dzong of Bhutan, and is quite a beauty indeed (see the picture). It is the only dzong that is not located on a mountainside or -top, sitting flat between two rivers. It's the most symmetrical of the Dzongs, and seems to be quite well restored. If you can only visit one dzong, I would recommend this one for the biggest wow-factor.
• Wangdue Dzong (The destroyed one): This dzong burned down in 2012, and is still being rebuilt. I only looked at it from outside. The back and front part seems to be already finished, but the middle is still in ruins. A visit does not seem to be possible yet, and I can't judge about the quality of the restauration. I would expect a fine and faithful rebuilding, as the bhutanese people are quite serious about their dzongs.
• Trongsa Dzong (The large one): Advertised as the largest dzong in Bhutan, the dzong sits on a very nice location, overlooking a deep river gorge. Its external watchtower houses a nice but small museum of royal insignias - not really a must-see. The dzong looks best from the outside, its inside is fine but not as impressive as the Paro/Punakha dzongs. Trongsa is located quite a bit to the east, and you will need multiple days to reach it from the airport.
• Dagana Dzong (The unknown one): I have not visited this one, as it is not located on the typical tourist route, which goes from Paro to the east. I couldn't find much information about it, and it is not heavily advertised. The photos look impressive, though.

All in all, the dzongs are very worthy of being a WHS - the only question remaining is: Why are they not on the list yet ? I can't imagine any opposition against their inclusion.
Visited in November 2019.
Importance 4/5 Beauty 5/5  Uniqueness 4/5 Environment 5/5 Experience 5/5