No doubt you're right that it would be more efficient to store the binary representation natively, especially assuming portability isn't an issue, and especially if a zero-copy solution were used, but many real-world systems have to cope with data formats that aren't the most efficient. Huge amounts of data are shipped as XML and JSON.
Both representations should lend themselves to compression.
True.
> it's hard to make a point that they occupy less storage
No, like I said, it would occupy less storage for sparse data. That's true even with separator characters (2 bytes as against 4). Doubtless there are much better solutions for representing sparse data that aren't human readable. A simple (index, value) dictionary, say.
> it can represent infinitely large numbers
Right, there's no upper bound beyond the limitations of the systems, although again a non-human-readable bignum format could do this more efficiently.