That’s basically what the U.S. is doing, and you can see where it’s gotten us. :)
If you pay off your debt, there may be a time without debt. And then you have all of your resources at your disposal, to use as you will. You might even be able to retire if you have saved enough, and not have to work at all unless you want to.
The worst-case scenario is like the opposite of this. Because you will always be paying more money, you will always have to work. Because minimal payments may not even cover your interest, you may owe more every month, and if it hits the limit and goes over, you will owe even more. This will cause your minimal payments to go up and will give you fewer options for gaining more credit in the future. And this way, you could be paying for a small purchase for the rest of your life. Imagine being 80 years old, unable to quit working, and then something happens – you break a hip or something – and then everything spirals downward from there.
That said, credit card companies LOVE when people only pay the minimum, because they make the most money on people like that. It’s people who pay off their bill every month and pay no interest that they hate. And something about being Visa’s favorite kind of customer chafes me.
Just pay ‘em off. Pay it all off. Stay out of finance hell.