William is not a thug. He got pissed off at Harry being a dick, there was no reasoning with him and because William cares deeply about his brother, his family and the institution and because he feels all that responsibility on his shoulders, so he saw red when his beloved brother was being so pig headed and probably extremely rude and provocative about William's wife.
If anything this makes the royal family more relatable. They are royal because the constitutions says so. Until that changes the RF just is, whether we like it or not. If they are human and experience anger, jealousy, worries, bullying, sickness, death it makes them more relatable, not less. The RF fulfils a function, both historically and, while we have a monarchy, at present and in the future. There are many parallels with ancient mythology and the RF represent more than just the collection of imperfect individuals.
Just because some people are monarchophobic and Harry is trying to take advantage of that, it doesn't mean the British public will get rid of the monarchy anytime soon. As we can see, they provide huge entertainment value, if nothing else. So, in some ways, Harry is doing a great job as the spare, he has chosen to play the role of jester (again lots of parallels with antiquity) and is providing much needed belly laughs for the population at rather dark and gloomy time. Those Spanish translations were the funniest. I mean he uses the medium his auto-biography to declare that he mounted a horse loving older woman, and let her spank him after the deed?