When mixing our first EP, the band wanted to hang out in the rehearsal studio and just listen to the rough mix on the PA. I wanted them in my "studio", or at least my car. They asked..."The PA is for music. Why can't we listen here?"
I said something about fidelity and frequency response, and PA cabinets aren't for listening to music like this...and then offered them beers and they forgot the question.
What's the better answer? Why is a nice set of small speakers good for mixing, but a big set of PA speakers are not but the PA speakers are good for live music?
There's actually quite a lot to unravel in here, part of which has been addressed by Richard.
The point of well-designed monitors is to reproduce as accurately as possible what you've recorded. Interestingly, that is also the goal of well-designed stereo speakers, including PA speakers. The extent to which any do this depends on the level of engineering in the design and the quality of components.
The conclusion you can draw from that is that, all things be equal, there is nothing intrinsically 'bad' about listening to a mix on PA speakers. However, given the comparative outputs of monitors and PA systems, the power required to drive each and the cost of delivering that power accurately, it is more than likely that the monitors are going to deliver the mix more faithfully than your average PA.
But I can understand a desire to listen to material through a PA. There is that psychoacoustic excitement when listening to things loud. The danger, though, is that this excitement can disguise flaws and make things sound better than they actually are.
There is no harm in listening to mixes on lots of different systems. But there is a drawback. What happens if it sounds good in the car, but not through a boombox (or vice versa)? If the studio monitors are reputable, and you trust the ears of whoever is doing the mixing, then you should be able to discount having to test it elsewhere. Every listening environment is different, and trying to deal with the variations in these by listening within those environments, then going back and adjusting in the mixing environment, is a quick path to frustration.
If the monitors are just ok, and you are not sure how well the person doing the mixing is coping, then checks on other systems are worthwhile, in that they may reveal a systemic flaw in the mix (e.g. universal too much bass, or too much treble, or vocals too soft).
