Serious question. I'd especially like to hear from those of you with extensive FOH experience. 
 
In my experience, PA systems generally sound bad. In the 60's they weren't powerful enough. In the 70's they compensated for that by stacking ever-larger piles of speakers and amps, but all it did was get louder - at least, for the audience close to the stage. Those in the back still couldn't hear it. Subwoofers made their appearance in the 80's, extending the frequency range but also assuring that the folks in the back heard amorphous mush, but with bass. In the 90's we saw the arrival of arrays, which helped with coverage but did not sound any better. Nowadays we have high-tech computer-controlled systems that can compensate for different-shaped rooms and avoid feedback. But they still range from just OK to unlistenable.
 
What prompted this rumination was going to see Rain (the Beatles tribute band) last night. It was an acoustically-treated 1,500-seat theater, and a full house with 1,500 acoustical absorbers in the seats. A lot of thought had gone into putting that show together, and it was top-notch in every regard but one: the PA. It sucked. Surely, an act that went to such lengths to put on a great show would do anything they could to make it sound as good as possible out front. But it sucked. It made me sad.
 
So why do you think live hi-fi sound is such an unattainable goal? Is it physics?

ALL I KNOW IS....
 
i spent 6.5 years full time on the road,
and part of my responsibilities was helping setup and tweak the PA (in addition to setting up our light show, that's another story)
 
we purchased a frequency analyzer,
that would put white/pink noise thru the system,
and would help us EQ the system flat.
 
it had a memory, and at least two memory presets.....
we set up for the room empty,
then on the busy nights, we would tweak the room EQ until it was dialed in,
mid week we would do a quick 're-set' using the two EQ settings to find the happy medium.
 
this was a full range 4-way PA, with 18" folded horn cabs for subs, 12" drivers for mids, horns for high mids, and bullets for highs.
 
we ran it with Crown and Yamaha Power amps, we had TONS and TONS of power.
 
we ran a 24 channel allen and heath board, with 31 bands on the pa, and 31 bands on the monitors,
which had their own mixer and power amps.
 
 
this system ran like a charm, and sounded awesome always.
well, almost always.
 
LOL
 
there was always a 'room of doom' that had such terrible acoustics, that nothing could be done,.
 
 
i say, if the PA sound bad, it starts with the soundman,
sits in the middle with the quality of the gear,
and ends with the room acoustics.
 
 
2 of those you can fix.
 

I think rock music sounds lousy in large (even semi-) reverberant spaces.
 
Symphonic music is a totally different story.

Everything Bat said.
 
The main issue in the past was simply that high power PA speakers sounded awful.  Seems you could have quality OR volume, but not both.   I was always told it was because they gained extra volume by using "tuned" cabs,  which is fine for subs but leaves holes and peaks in the spectrum for Mids.
 
It has been well known and accepted for a long time by all manufacturers that PA does not equal HiFi and us poor FOH girls are left to fix the mess with pink noise and GEqs.
 
Things are starting to change though with more emphasis being placed on quality by the PA manufacturers.  I know I keep banging on about Presonus...  but it's what I've got and I know what it does, but take it as an example. (Other manufacurers are available) Their new PA range (designed by WorxAudio I think) was designed from the start to give HiFi output at PA volumes.  The cabs are active (so no chance of messing up the sound with impedance mismatches) and include DSP that gives 31band GEq, 8 band PEq, and delay.   All the drivers are coherent phase matched, including when linking to the matching subs.  There is all sorts of software trickery going on.
 
The net result is not what you'd expect from your home audiophile HiFi, but it's a darn site better than we had in the past.
 
 
The thing that Bat missed though is audience expectation.  Since the introduction of subs, people expect to be able to feel it as much as hear it.  To me, this is the main difference between a rock gig and a symphonic gig.  For symphonic you're trying to boost the volume while maintaining as much clarity and quality as possible so you're not altering the original sound of the instruments.  Whereas a rock gig, the FOH engineer is as much responsible for creating the sound of the band as the musicians, if not more...  and the audience want that "live" sound.
 
I mostly work with cover/tribute bands and most of my job is to make them sound like the band they're trying to emulate.  As long as they can play the right notes at the right time the sound is down to the FOH eng.

All I know is that great FOH engineers are magicians. I realized this when one of them turned me into a newt.
 

 
I got better.
 

 
See?

Anyway...
 
I know what you mean about the sound. A very long time ago (1982), I saw Asia perform at the Auditorium Theater in Chicago. The venue was not normally used by rock bands. The urban legend stated that the management of the Auditorium Theater chose not to rent their hall to rock bands due to the destructive nature of the fans. The acoustics in that place are fantastic. That night, the band sounded incredible. The sound was crystal clear. I had never heard such a great sounding live show. 
 
After attending many other shows in venues large and small, it became obvious that this was not a technology issue. I saw Rush play at the United Center in 2002. The place is a gigantic barn. It's designed for large sporting events, so the acoustics are beyond terrible. The sound of the band was unbelievably good. I was shocked at how clear everything was and how I could hear absolutely everything in the mix. It was loud, with chest thumping presence, but not fatiguing. It was nearly perfect. A year or so later, I saw them perform at an outdoor show. The sound was horrible. Lower mids overwhelmed the other frequencies. Audio in the 3khz-5khz range frequently vanished and piercing spikes around 12khz made you wince. It was nearly unbearable.
 
The FOH engineer can make or break the show. A great one will make the band sound their best. A bad one will make them sound like a bad garage band. It's not about technology, gear, or software. Truly great engineers have the best hardware between their ears. 
 
 

That must be where I'm failing,  it's mostly soft between my ears..
 
 
Outdoor gigs are HORRIBLE for a FOH eng.  The different freqs can be blown around in the wind like smoke.  It all down to variable air density..
My favourites are outside, but in a large marquee.  You get all the advantages of being outdoors, no reflections, almost no noise limits, and all the advantages of being indoors..  no wind, no rain. (Just watch for rain collecting in sags in the roof...)

Karyn
The thing that Bat missed though is audience expectation.  

no, i didn't miss it, and the band as a whole, was very aware of 'perceptions' of 'proper' mixes, versus proper mixes.
 
LOL
 
a lot of times, the success of the band in a club, as entertainers, has just as much to do with having a good full range sound at a LOWER volume so that the waitresses can hear their orders, and so that the glasses don't rattle at the bar.
 
LOL again....
 
there are so many variables that go towards having a 'good gig', besides decent sound.
 
 
but, fact remains, we always worked hard at finding the best compromise, 
and for most good soundpeople, that is the task
 
too much low end sux,
and that is the single biggest complaint i hear from almost everyone i know.

also, the low end problem usually comes from having the wrong kind of low end, subs in particular..
 
i mentioned folded horns with 18's, 
that's because we were playing bigger clubs.
 
in smaller clubs,
we actually had 'sugar scoops' that used 15" front mounted,
and those kept the low freq's from trying to drive thru the back walls and out into the parking lot.
 
 
low end freqs take room,
and in small clubs,
it never comes together.
 
 

What I meant was, there are good mixes, "proper mixes", and "audience expectation".
 
For most Rock type gigs nowadays you get a slight lift around 100 - 150 Hz built into the PA by default.  If it's not there the FOH will add it to the main Eq.  It gives ....  ummm...  whooomph!! to the kick and bass and came about when we started adding subs to standard systems without proper crossovers.  Yes, the sub extends the response down to 40 Hz, but you get a boost at the overlap.
It's that sound that audiences have come to expect, rightly or wrongly.
 
Of course, it's different rules altogether if you play synthpop or classical...