Dave Ramsey (like others have said) is a great authority figure for people who have zero financial literacy. His main audience is Average Joe who has paid a whole lot of "stupid tax" by buying things without being able to pay for them, and getting stuck in consumer debt.
If you have any sort of self-control and the ability to do basic math, you have outgrown his teachings.
The snowball method is great for people who need to see accounts close before they "buy in" to financial competency and debt reduction. By the numbers, the avalanche method (highest interest first, balance be damned) is the smarter way to go, but it's also not as rewarding as completely getting rid of smaller balances (with lower interest rates). And if you can't own a credit card without racking up debt, then cutting them up is better than opening up that door again.
That said,
He is a great authority figure. My significant other is a spendypants "normal" person who has a bunch of consumer debt, car loan, student loan, etc. -- I started listening to Dave Ramsey all. the. time. because my approach to finances isn't compelling to him, and doesn't see me as an authority figure on money. So I started playing the podcast in the car. Streaming it on youtube when I was cleaning the house. Left a copy of the book lying around, and my SO started to become interested. Now, we have a debt-reduction chart on the fridge, he's snowballing his debts, and is feeling accomplished. So it's working as intended! And the book definitely helped.