In no medium until the CD has it been possible to store a dynamic range compressed audio without giving up something. On vinyl, a loud mix means less audio can be stored, while it doesn't matter on a CD.
This is a bit off base. The "loudness" of a vinyl recording has to do with groove depth. "Louder" audio has nothing to do with how much audio could be stored, which is a function of groove width. Also, the whole point of dynamic range compression is to improve audio fidelity in lossy systems such as tape decks or radio broadcasts. That's why u-law compression is built into our telephone standards, with a compressor on the transmit side and an expander on the receive side.
The other effect is what makes tube amps "better" as well - what happens when you overdrive them. A vinyl record when clipped doesn't hit a hard stop - it hits a soft stop and ends up distorted. Ditto a tube amp - overdrive them and the waveform distorts. However, do that to a CD or transistor amp, and you get clipping. The harmonics induced by clipping the audio are far more harsh to most people's ears than the soft-clip distortion you get with vinyl/tube.
Also why some of the best guitar FX pedals use tubes in their final stages - you want that nice distortion, tubes are really the only way. The alternative is to waste a lot of ADC/DAC and DSP processing power by not using the full dynamic range so there's no possible way to clip, and then process the signal to add soft-clip effects.
There's nothing magical about vacuum tubes. They amplify and clip according to physical processes, and can be described as mathematics just like anything else. An ADC -> DSP -> DAC system is more power efficient, more easily reproducible, much more reliable, and more rugged than any tube-based anything. Ponder this - if you were looking for a specific sound to add to your guitar playing, wouldn't you rather have something _specific_ and consistent from use to use than something which is temperature-dependent, age-dependent, and tube-brand dependent?