Why bother stripping them of anything???? There are over 500 people in line for the British throne. Does it matter that there is 10 in line for the Swedish??
If the king planned to strip his grandchildren of their title, he wouldn't have given it to them in the first place. It isn't like Madeleine suddenly decided to leave Sweden recently and things needed to be reconsidered. She was living in NY when Leonor was born, and there was no reason to believe she would be in Sweden. The king is the one who funds or doesn't fund his daughter, through the money he receives, Madeleine herself doesn't receive funds. Really the king is the only one who can complain about the finances.
How is it going to help Madeleine live a private life? Madeleine is always going to be a princess of Sweden. That will keep her in the spotlight. The interest is in her and not her kids. Having them have no title is not going to allow them more privacy. Madeleine would have to change her name and disappear for her to have privacy. And why should she? She has her work with childhood, and is entitled to her place as a Princess, as CP is.
Madeleine was raised in Sweden, is a member of the Church of Sweden, got married with the Swedish government's consent (granted upon the King's request), and is not the sovereign of any foreign country. She cannot be legally removed from the line of succession then. The issue is not Madeleine's succession rights, which are secure, but rather her children's.
The question of titles is somewhat more confusing because there is no clear statutory instrument regulating the titles of the Royal House of Sweden. As I interpret it, before 1980, princes and princesses of Sweden by birth were all male or female descendants in paternal line of King Karl XIV Johan unless they violated some provision in the Act of Succession. Note that the provisions in the Act of Succession were not exclusively related to succession rights per se, but went beyond that. For example, royal princesses of the blood were not in the line of the succession, but, under the Act of Succession, they still couldn't marry unequally or, else,by implication, they ceased to be princesses of Sweden as was the case with Carl Gustaf's sisters.
Post-1980, on the other hand, except for living people who were already HRHs at the time (such as Princess Birgitta), princes or princesses of Sweden are now all descendants (in male or female line) of King Carl XVI Gustaf, unless they violate again some provision in the (amended) Act of Succession, which now also always implies being excluded from the line of succession . In other words, as I see it, the title of prince/princess of Sweden and succession rights come together now.
The royal duchies, on the other hand, are a different matter as, although being an HRH seems to be a necessary condition to get one, it is not a sufficient condition and it's up to the King's discretion really as the duchies are honorific titles of the Royal House.