All pop/rock music is compressed otherwise it wouldn't sound as good (or bad :). Try recording live drums and electric guitar,keyboards etc without compression and you would either one huge distorted mess or to minimise distortion it would be too soft/quiet to appreciate. The sounds have to be squashed in order to make them as loud as each other without losing their intended impact. Acoustic instruments are different because you can gage the dynamics/peaks with mics before you record and then mixing is all you should need to do. Although most drums would still need to be squashed into a pleasing noise to fit the picture.
Its a very hard recording practice with classical music trying to replicate that live performance and to be true to the natural dynamics, but even then you will still most likely have to use some compression with brass and timpani for example. But as a general rule recorded classical music is the best for dynamics if you want to test your equipment.
With Radiohead you have such an array of sounds from acoustic to electronic, they make musical soup! If no compression was used it would be un-listenable. It's as dynamic as it can possibly be though, as that is the job of the producer to do this. To be fair Radiohead albums do actually sound very dynamic compared to most pop.