I think the Royal Family probably think that by keeping traditions going, they are keeping the institution going and preserving a formality which is useful for our country, in the operation of constitutional affairs when you want an official and ceremonial side. They seem to see continuity without too much change as a positive aspect of preserving the higher values.
I suppose knowing the Royals are formal is better than thinking that they shut the doors, slump back on the sofa, and say to each other: "Well that was a pile of tripe, having to talk to those boring councillors. How long is it before we have to do one of those tedious engagements again? The pretence is doing me in". At least we know that they believe in it all.
It's a bit like Church, where you genuflect, if you are a Catholic, or you line for communion and do the same things in a certain way. The forms are thought to help preserve the seriousness and sense of responsibility which is attached to the greater values of the institution. I have a friend whose husband is a reverend. She refers to him as 'Pastor' - she says 'Pastor was asking after you', not Tim was asking after you. It isn't unprecedented to see formality carried over into some of the forms of relationships. If you marry into a family which has a set of values, then I suppose you accept them, or choose not to marry in.
There are plenty of photos of the Queen going to kiss a young adult Harry warmly on the cheek, or letting a smile escape when she is inspecting a line of troops of whom he - her own grandson - is one. We know that she could and did display warmth to her family members.
Since his stint on I'm a Celebrity, Get Me Out of Here, wasn't a disaster, I'm minded to take back my opinion that Royals will struggle to get a show like that right, and to wonder if it wouldn't be a bad idea for Mike Tindall, that ex English Rugby tough guy, to give his take on what it is like being in the Royal fold at Christmas and having to bow and maintain formality.
He seems to be doing ok with Royal forms, and the experience hasn't changed him, judging by how he behaved on I'm a Celebrity, f-ing away at times, and being his comfortable self. The Queen was said to enjoy the company of Zara and Mike pretty much above that of all her grandchildren. Harry has said he has chatted to his grandmother telling her who to watch out for and who to take advice from, so she was ok that with that degree of assertiveness from a younger relative, and can't have been that forbidding.
Anyway, I doubt if the ceremonial part of Royal traditions would really be the thing to give you stress. I don't really know why it's worth revealing the curtsey episode. If I'd married somebody whose father was a free mason, and he was weirdly secret about what they do in the Lodge, and disappeared off to another room to learn things for his next meeting, I don't think I'd either tackle him about the ridiculousness of the secrecy and ritual, if I saw it that way, or berate my partner about it. It's just their choice. Families have things that seem odd, but it's usually possible to go along with certain things and maintain your essential integrity of who you are, the way Mike Tindall must have done and for whom the etiquette was probably a million from what he was used to.