A cynical commentary follows.
I didn't see the programme so cannot comment on these two people directly. However, not dissimilar types are excellent or in truth not at all excellent examples of modern social conditioning and why since the 1960s there has been a very good reason to stay single. First, many couples are under each other's feet for far longer than would have been the case in earlier history. A lot of them will negotiate that fact by focussing on work and eating and in their leisure time by going into separate rooms where one watches football and the other talent shows. Once the kids have figuratively grown up and gone on to study knitting or gaming at university while leaping in and out of each other's beds and sex clinics, they will recognise that they have nothing much in common and conclude they never did apart from in the sphere of sex as they imagine or imagined it. In a sense, they will know it already but can't bring themselves to admit it as they have to keep the family together. For this reason alone, sex is elevated to become the major issue as subconsciously they feel it is the glue.
Beyond this, both will view sex as being highly significant anyway because of its media and social presentation. It has been this way since the advent of the pill and other contraception and all that went with those developments including sex as selling. That was really the moment when there started to be huge pressures on both genders to be sexy by which society meant what it considered physically attractive even if in personality terms it was accompanied by very little or nothing. It was a sort of cultural aryanism, not that this implies fair haired and fair skinned but rather the so-called strong and beautiful, so that from this period no one who failed to look like a god or a goddess ever got together happily as before. That is, on the simple grounds that they ended up together at a dinner dance and mildly enjoyed a one minute waltz.
Arguably, the greatest pressure was on men but only marginally, that is, until a whole raft of additional measures for them to get things right was introduced with feminism as that too emerged in the late 1960s. Feminism has come in ever greater waves and we are living in the latest wave now. But irrespective of the social changes in the 1960s already outlined, in the so-called old days a husband and wife very often didn't see each other for four to six years at a time as the men were in the army or the navy generally fighting wars. It wasn't simply that every shag minus contraception led to more responsibilities. Consequently during the five hours in any decade that they did spend time together, sex was fitted in naturally and basically linked to procreation. It was when the kids were conceived before he went off again to risk his life and she would make blankets for men generally on the frontline in the vague hope that some would return alive.
Then, what you have is a sort of tacit acknowledgment from both of them that the modern discussion of rape could be helpful especially to her when she decides ultimately that she wants out. For as long as he is asking, she can't claim that he was anything other than respectful and even with the easy divorce legislation being brought in he might still be able to say they should stick together. By insisting that he doesn't ask so long as he doesn't force her, she can acquire the intimidating power of one of the world's more authoritarian leaders and always say that she was forced at a future moment of her choosing. At that point, she is free as she sees it so it is effectively an insurance policy for her abandon.
Finally, both are in the modern category of wanting an audience to their sex lives so that they each feel special beyond how they actually feel in regard to each other while simultaneously and somewhat irrationally thinking that to have an audience is the new normal which by definition would mean that there is nothing special about them at all. The proof of this is very clear. Where there is a genuine concern, a counsellor will be seen in private. Where there isn't, a couple will take their so-called issues onto national television and spend the following week in different towns from each other reading how they did in the ratings. That instinct will be fuelled in both of them probably by a knowledge of, and their own audience to, singles on social dating sites and pornography use which run in parallel to what they believe is a relationship. In those they can go into a fantasy world of still actually being teenagers with aspirations so as to pretend away their own aging process and mortality. The pictures are especially wonderful as they imply an absence of germs and sexually transmitted diseases in what society has decided are good looking people so that in parallel the prospect of arthritis, dementia and worse in older life can also be pretended away. It essentially says to them illness can't exist.
Obviously, their boredom and sheer states of being boring even to each other could be easily addressed away from any cameras by taking to separate bedrooms in the night and developing mutual interests during the day like pilates, pot holing and philately. In fact, they could learn together how to stick stamps in an album while attempting to crawl through dirt tunnels in the lotus position, alternating consensual activity with a mixture of civility and, if she agrees, inelegant brute force. Sure, it would remove the troubled film star elements to their lives and as a consequence for quite a while it will seem entirely unreal. In parallel, he will feel sexually impotent and she will feel very unpretty even if they have already brought enough children into the world to fill a cruise liner. Their concept of parenting may also change in this transition. Rather than it being a subconscious wish to have adoring and/or outraged observations from parental types to their sex lives at the age of 42 it might actually cross their minds that the parental role should be fully in themselves. But whether their greater interest in their own children's lives will be good is debatable, not least I should imagine to their children.
Modern marriage (which bears no resemblance to marriage as it was from the 1100s to 1965) is ironically the only thing which extreme fundamentalist Islamists and gay people both now support. The very fact of that counter-intuitive and solitary consensus should tell everyone else a lot about the nature of being misguided by - and even victims of - what has been policy set by failed British governments ever since Mr Wilson's. In contrast, China seems to be doing rather well.