> I know this is a big claim

Perhaps, but it needn't be to get the same asymptotic performance.

Okasaki's simplest random access list has performance proofs that depend only on the simplest properties of binary numbers, rather than those of the Exponential-Golumb coding, and the code is very easy to write:

    data BRAL a = Empty
                | Full (Maybe a) (BRAL (a,a))
                  deriving (Show)

    cons :: a -> BRAL a -> BRAL a
    cons x Empty = Full (Just x) Empty
    cons x (Full Nothing ys) = Full (Just x) ys
    cons x (Full (Just y) ys) = Full Nothing (cons (x,y) ys)

    nth :: Integer -> BRAL a -> a
    nth 0 (Full (Just x) _) = x
    nth 0 (Full Nothing xs) = fst (nth 0 xs)
    nth n (Full (Just _) xs) = nth (n-1) (Full Nothing xs)
    nth n (Full Nothing xs) =
        let pair = nth (n`div`2) xs
        in if n`mod`2 == 0
           then fst pair
           else snd pair