Immediately paying off a card doesn't build your credit much. All creditors look at your credit report & score, and one of the things the report mentions to them is whether you are able to take out a large amount for something (i.e. purchasing a TV, computer, etc.) with your credit and pay for it over a period of time. Sure, you lose some money this way in the short term, but in the long term it means you will save a lot more in interest when you finance the purchase of a car or take out a mortgage to pay for a house.
In addition, if your one credit card gets stolen, then you can be in a tight spot in terms of daily expenditures until you get your replacement card. Or if one card gets compromised somehow, then you have no other to fall back on. And lastly, having only one line of credit open doesn't look very good to creditors.