I think a part of it is there were already friendly before they married so they obviously have a lot in common. Also as Joachim has quite a low profile and M&F are the real 'stars' of the show it couldn't be said Marie was just after fame/attention.
I bet part of why they are so happy is that Marie appeases Joachim quite a bit, I imagine he is quite a strong character with set ways/opinions and she probably spends a lot of her time saying or thinking "yes dear", but if they are happy then great for them!
It is well known from interviews that Marie is an equal partner and a strong women that gives Joachim at times a run for his money. They both have character and class when it comes to their marriage - and what seem genuine love for one another which reflects in their children and step-children.
Joachim's & Marie's profile is kept artificially low, because it would become painfully apparent, that Joachim & Marie would be the logical Crown Prince Couple, standing out by upholding Danish interests, Danish tradition, work ethic, and Royal decorum.
But as it is sporty, lazy Fred won the vagina lottery, alas is the CP, that in turn married a liar, a thief, a manipulator, and a pretender and made her the Danish Crown Princess. If you call that a real 'stars', then by all means, Denmark has them.