> and there's no discernible compelling advantage
Actually, for wire encodings, there is, although I've (I-think-)literally never seen any proponent of big endian bring it up (versus the bullshit "it's human-readable" nonsense[0][1]): big endian encodings of unsigned numbers have lexicographic order that matches their numeric order.
The most obvious concrete example of why this is useful is a keys-sorted encoding of a hash table: if you encode keys in size-type-value format, you can check sortedness by lexicographic order of type-value strings (which means you can add new types without old software needing to know how to compare them), and you'll get integer keys in inspection-friendly numeric order rather than semi-random order. (Encoding negative numbers with a type id of T_UINT-1 lets you extend this to them as well.)
At a more abstract level, where (zero-padded) little-endian numbers have the same value at different granularities, this means that big-endian numbers have invariant lexicographic order at different granularities: two strings viewed as bits, bytes, or uint32s are consistently in the same order.
You can kind of use reverse-lexicographic order for some of this, but there are obvious problems with sending data in value-type order rather than type-value, so forward-lexicographic tends to be strongly enforced.
0: "You mean for arabic numerals, except not actual arabic numerals, because Arabic is written right-to-left, so the numbers are little-endian there, but ended up big endian because they stayed least-signifiant-digit-right rather than least-signifiant-digit-first when imported into Latin."
1: "Also, so (supposedly) is decimal and sign-magnitude, but we've (agonizingly slowly) learned that those aren't good ideas."