Simply having the money provides you with the income to not only pay the interest, but to accumulate more money (that accumulates more interest, etc.). Even if you're so incompetent that you can only get a 3% rate of return, that $1 million would return $30k per year. You are only paying $9,900 in interest on the loan. That means that you're pocketing $20,100 per year.
Obviously, this is not a real world example. But it's an example that makes the complex simple. Because this sort of calculation is exactly what you should always be doing. If you have credit cards that are only charging you 3.99% interest, then you shouldn't be paying them off. If your mortgage loan is 4.25%, then you shouldn't be paying that off. Why? Because any idiot can get a 7% rate of return on his investments by simply dumping all of his money into an S&P 500 ETF and setting it to automatically reinvest dividends. You never have to touch it, never have to know what you're doing, and you're making more money than you would save by paying off that debt.
This is why idiots like Dave Ramsey shouldn't be giving people financial advice. They don't teach the above. Instead, they tell you to be debt free, even though it may be costing you a ton of money to do so. You should do whatever it takes to maximize your net worth. That is what ultimately brings peace of mind.