That would be very difficult to do, without losing control over the balance of the entire mix. You could record the quartet with 2 overhead microphones, using AB stereo techniques, or even a coincident pair, but the finished recording would sound very different to what you might hear were you actually listening to the performance in person. The human ear is an amazing device, it allows us to discriminate between all manner of sources of audio. Once you record that same audio, with whatever technique, that ability is mostly lost. Binaural stereo might be one way of preserving this, but not everybody wants to wear headphones all the time, and the technique does not suit everybody.
Close-up micing is normally the best technique to use, since it allows the engineer complete control over the final mix, and the ability to compensate for any differences between what is recorded, and what is performed.
The harmonics of brass instruments probably come easier to the valve users whereas it's probably a bit more of a challenge for the SS guys. 
