It's true, programmers tend to be better paid. (I'm a game artist that worked for 4 game companies) .But I highly disagree with above poster. We're talking about a professional programmer and so, also about a professional artist. Ok, then just drawing well requires a ton of years. I mean, just draw correctly with good anatomy and proportions, solid perspective, good control of lighting, composition, etc. This requires a career, usually(and many extra years on your own, and even so, many don't reach the level). Be it Fine Arts, or what is being done in USA and Canada, special institutes to prepare ppl to do concept art and have the needed base for modeling characters of the high realism you see in any high end game. (millions of polygons for detail is not all, there's needed a lot of knowledge and techniques behind, that all is hyper realistic, does not come free, and only a few artists get it right)
Let alone the fact that the "modelling software" training is huge in years. Master Uv Mapping, high end modeling, texturing, shaders, GUI work, pixel art, etc,etc. (I'm proficient in all this) Animation in its own is a very hard career, and I can tell how few good animators are out there, that can animate really well, at the needed quality.
But it always keeps floating this wrong concept saying that salaries are ok so because programing (extremely hard, too) is harder. I have known of the years and preparation needed of way too many staff mates, and man, compared with my close to 30 years of real preparation, is at least, on pair...
IMHO is just a market reason, a matter of how many are out there, and certain historical reasons.
Edit: And btw, you mention musicians, they are even paid worse than artists. And again, is not a matter of they had less preparation. Again, is market reasons, number of ppl into it, etc. And to your question: "And sometime I wonder even if an artist can happen to write scripts..." I am a game artist, today a corporate designer, and yep, I have coded scripts, VB, html/css, some action script, some python... A practical advice would be: become a programmer, as the market needs more them, as there might be fewer programmers into games (and yes, an incredible amount of knowledge is required).