Lilianne Bettencourt is under conservatorship now. But she is to be credited for picking the CEOs which enormously expanded L'Oréal (François Dalle and then Lindays Owen-Jones).
Now her eldest grandson, Jean-Victor Meyers, holds the reins, picks the CEO and is very much hands-on (last time I checked he was visiting plants all around the world).
But with a net worth of 90 billions (and they are just 4 people), they have absolutely no reasons to sell anything. Plus Nestlé (yuck) is the second shareholder and they have a shareholder pact (which possibly include some call or put options).
Potentially, it could become YSL Beauty or Valentino Beauty by Nestlé Beauty (yuck again), before LVMH or Kering could move.
I am reasonably certain there is also an agreement between Armani and L'Oréal for when the maestro will pass. The Meyers and the Armanis are very close now, even vacationing together.
I agree Kering lacks a lot of in-house products like: joaillerie, high joaillerie, haute couture, beauty... and they lack strategy, mainly because they have no vision, and only see the next two quarters, while LVMH and Hermès strategists think 2 decades in the future.
Chanel is also guilty right now of having no vision, the Wertheimer bros never had one and are vaguely interested, the real thinker also was Eliane Heillbronn, and all the very good people she picked for Chanel (who now must be disappointed by the state of the company, see Maureen Chiquet going to be board member of Kering)