Maybe 'ridiculously fragile' is the wrong word. Perhaps 'needlessly' fragile would be better.

The point is that it takes application of algorithms that need to be provably correctly implemented on both ends of any JSON serialization/deserialization. And if one implantation can roundtrip its own floating point values, that's great - but JSON is an interop format, so does it roundtrip if you send it to another system and back?

It's just an unnecessary layer of complexity that binary floating point serializers do not have to worry about.