I would recommend programming, just because it's the only way to implement your own ideas. Otherwise you're at the mercy of whatever programmers you can manage to get.

I believe it would be better for people to work as a team when trying to make a game.

Sure, making your own game from scratch by yourself is good for showing off your "1337ness", but does that really prepare you for the game industry? The answer is no.

With new technology and ideas being used everyday, it is best to have a team to make a game that is very competitive with other games. It is also best that you are a team player. The owner of a company wants a game that people would be willing to throw away 50-60 USDs on even if it is just freeware. After all, he makes money off of you. He sells that product to a manufacturing company that hopes to make mega bucks off of what was initially made selling it to distributors.

Your software development boss gets a residual income from what is sold and you only get paid for the work you did. In the end, the programmer gets financially screwed even if he's getting paid 50k a year (unless he is really good with people, really likes his job, is willing to wait for his spot in climbing the ladder, and is lucky to not be fired because of downsizing).

I personally don't want to put up with all the office bull along with deadlines -- people telling me when I can eat, when I can use my skills and how I should use my skills. After all, it's my skill; why not use it making something that I love?

Being a programmer at a job gives you a skill, it won't make you rich. Bill Gates is rich because he's a business owner, not because he can program.

Now if you want to learn how to program as a hobby, go ahead, you'll enjoy it more and will probably learn more along the way, but if you want to make money, you need to learn how to market your services, or get with me -- I'll show you how to make money another way. I work with very credible people that can show you what I know.

Now don't get me wrong, programming is great, and I encourage people to learn it, but I would never recommend someone to learn programming to get a job, it's just too painful for those people in the end. I show people how to become business leaders and if you want to program because it's a well-paying hobby, then go do that.
There are only a few people in the world that have programming as their calling. Other people just want money to pay the bills.
I say follow your dreams. Know what you really want in life, and achieve it.