It still doesn't pretty well on text. And we have newer formats and ideas that would also deal with that. (To be really dead simple: have a minimal container format that decides between png or jpg, use png for text.)
However: white noise is where it really struggles. But real pictures of the real world don't look like white noise. Even though in some sense white noise is the most common type of picture a priori.
Similar for real world time series: reality mostly doesn't look like white noise.
I have a very peculiar coin. With 1% probability it turns up heads and with 99% probability it turns up tails.
A string of flips is random, but it's very compressible.
In any case, my point was that reality ain't uniformly random. And not only that: pretty much anything you can point your camera at shares enough similarity in their distribution that we pretty much have universal compression algorithms for real world data.
However: white noise is where it really struggles. But real pictures of the real world don't look like white noise. Even though in some sense white noise is the most common type of picture a priori.
Similar for real world time series: reality mostly doesn't look like white noise.