(a) Potentially some space efficiency. They can't be fixed-size, but they can absolutely be a small number of varints (the standard zig-zag encoded 7 bits per byte with a high-bit signalling more data would be fine, or since everything in sight is unsigned you could skip the zig-zag).

(b) An intrinsic notion of order that is almost definitely correct. When the standard dictionary order suffices (actually a bit tricky with strings, starting with upper/lower-case and quickly devolving into questions of what an upper-case emoji is, but assume ASCII for the sake of argument), strings are probably a better conceptual fit. You'll struggle with the path-based approach when the number of dots changes though, when you have some concerns ordered monotonically one direction and others ordered the other way, when you need a notion of enough space to _always_ be able to slot an intermediate value in, ...