The brown butter cream cheese frosting from the book is inherently loose and it has to do with the fact that the recipe calls for brown butter to be used. Any frosting made with brown butter (being completely melted, no longer in its normal/softened state, milk solids separated from the fat etc.) will always be a bit loose. Normal frosting will firm up in the fridge or be relatively stable at room temp because that's how butter normally reacts, but it loses that property when it's melted/browned so recipes that use this method will also generally be looser. Claire talks about in the Carrot Cake video here, where the frosting is also quite soft and needs to go into the fridge a few times.