It's really hard to do live sound well, because there are a huge number of factors that make achieving the goals I laid out here difficult, including things like (in no particular order):
- Live shows often take place in large venues (i.e. arenas) which were designed to actually acoustically amplify ambient sound (for example, at a basketball game, you want the crowd to sound loud, not quiet). When loud concerts take place in these same venues, the system has to be designed to essentially to overcome these issues.
- Live shows often take place in small venues, where the sound coming from the musicians onstage is so loud that the sound system is often used only to amplify things like vocals and other "quiet" instruments. If the drummer is playing loud, then the bass player plays louder, then the guitar player plays louder, and then the sound engineer has to turn up the vocals to overcome all of those. It's sort of a nuclear escalation in that case, and the sound engineer doesn't have any fader on their console to make the drummer play more quietly.
- Sound itself is variable (temperature and humidity actually affect the speed and transmission characteristics of sound).
- Bands listen to a different (monitor) sound system and don't have any idea what their show sounds like to the audience. (Explained here)
- Extremely loud monitor systems (for hearing-damaged musicians) actually interfere with the sound that the audience hears, the same way as loud guitar ampfliers or drums.
- Band management, who may have hired the engineer, can tell him or her to do things that actually make it sound worse (i.e. turn it up to painful levels).
- There’s very little time in most concerts to install and adjust the system, and the audience actually absorbs sound and changes the sound in a hall once they are present. So, the sound check can sound different than the show.
- Since the musicians do not hear what they sound like to the audience, they have to trust someone. This might be their management, or an old, trusted, friend who may not have the technical chops to handle modern, high-tech systems.
- Sound engineers may be able to make it sound fantastic where they are controlling the system (the “mix position”). However, unless the sound system itself is engineered properly to deliver good sound to every seat, it’s quite possible that it sounds great at the mix position, and not as good at seats throughout the venue.
That's a start, let me know other things I'm missing.