Banks do not profit by your fiscal prudence
Banks are in it to make money. But they're expected to provide a social good which powers our economy: secure money storage (bank accounts) and cashless transactions (credit/debit cards). And the government does not subsidize this.
In fact, banks are being squeezed. Prudent customers dislike paying the proper cost of their account's maintenance (say, a $50/year fee for a credit card, or $9/month for a checking account) - they want it free. Meanwhile government is pretty aggressive about preventing "fine print" trickery that would let them recover costs other ways.
However there isn't much sympathy for consumers who make trivial mistakes - whether they be technical (overdraft, late fee) or money-management mistakes (like doing balance transfers or getting fooled by promotional interest rates). So that's where banks are able to make their money: when people are imprudent.
The upshot is that it's hard for a bank to make money on a prudent careful customer; those end up getting "subsidized" by the less-careful customers who pay fees and buy high-margin products like balance transfers. And this has created a perverse incentive: banks make more money when they actively encourage customers to be imprudent.
Here, the 0% interest is to make you cocky about running up a balance, or doing balance transfers at a barely-mentioned fee of 3-5%. They know most Americans don't have $500 in the bank and you won't be able to promptly pay it off right before the 0% rate ends. (or you'll forget). And this works - that's why they do it.
Nobody offers 0% interest otherwise - they'd lose if they did
By law, you already get 0% interest on purchases when you pay the card in full every month. So if that's your goal, you already have it.
In theory, the banks collect about 1.5% from every transaction you do, and certainly in your mind's eye, you'd think that would be enough to get by without charging interest. That doesn't work, though. The problem is, such a no-interest card would attract people who carry large balances. That would have two negative impacts: First the bank would have to spend money reborrowing, and second, the bank would have huge exposure to credit card defaults.
The thing to remember is the banks are not nice guys and are not here to serve you. They're here to use you to make money, and they're not beneath encouraging you to do things that are actually bad for you. Caveat Emptor.