You do remember its HER organization, right?
As I say, a club of people whom she happens to like.
and mages willing to push magic further.
Has Frieren not done that? If I remember correctly, she was the one to adapt Soul Track for human use, the most useful offensive magic of the current generation, and I reckon, her actively seeking out Flamme's magical legacy should amount to something.
Saying Serie is childish is just projecting your human value onto her, its like calling a meteorite immature because it does not care about property value and civil mayhem…
"Childish" is an evaluation of her reasoning ability. Any being with free will and agency to act upon it can be evaluated by how childish they are according to ours, human understanding of what being a child means. And I say, it'd more appropriate to evaluate reasoning ability of a thinking being who's not even driven by instincts unlike demons than to attempt to do the same for a flying rock.
Say, Frieren is the same species as Serie, and even if she's younger, she is unimaginably old for us humans. Can we say that her being a lazy ass who does not do her share of chores, has to be nannied by Fern, and impulse-buys magic grimoires because she wants is her being childish, or should we submit to the idea that she's as incoprehensible as a force of nature, and as such, we should not attempt to understand her using our human concepts? The latter would make this manga into a much more boring read if I am being honest.