Breaking things down to their basic axioms and rebuilding them with proofs is arguably quite an advanced approach. By Terry Tao's three stages of of rigour classification [0], this perspective isn't typical until undergraduate study.

It doesn't seem like a bad idea to give a taste of it significantly earlier, but I don't think it's surprising if someone without a more mature relationship with mathematics doesn't find much value in 'going back to basics.' If your daughter is doing well with a more intuitive approach it sounds like a good idea to stick with it for now.

[0] https://terrytao.wordpress.com/career-advice/theres-more-to-...