The money "freed up" by the snowball method was already being used to pay down debts.
Ie, imagine you have a pair of debts:
10k at 1% per month; min payment 200$
1k at 0.1% per month; min payment 100$
Free cash flow of 100$ (and 300$ which you are using to pay off the two debts; if you fail to make min payment, you get penalized harshly).
Snowball says "pay off the 1k debt first, as it is the smallest". And it is true that after paying off the 1k debt, you now have 200$ in cash flow.
But that min payment on the 1k isn't "lost money", it is being used to pay off a debt already. You are forced (by the min payment rules) to put it against the lower interest debt, but putting more money into the lower interest debt isn't the optimal solution.
Instead, you throw the 100$ at the larger 10k debt. Every 100$ you throw at it reduces its interest by 1$ per month, while 100$ thrown at the 1k debt lowers its interest by 0.1$ per month.
While it takes longer to clear a debt this way, you end up with more money at the end of the process.
You can flip everything on its head. Imagine if instead of debt, you had 2 investment chances. One can soak up to 1k, and returns 0.1% per month in yield. The other can soak up to 10k, and returns 1% per month in yield.
The second is clearly a better investment option.
High interest debt is toxic.
There are real advantages to snowball beyond the psychological.
Every debt requires effort to keep track off. Fewer debt, less tracking load.
Free cash flow can help avoid adding more debt, and min payments aren't usually linear. By clearing a debt completely, you can maybe avoid having to borrow to handle unanticipated problems.
If you do need to renegotiate or whatever, fewer counter parties makes such renegotiation easier. Like, if you owe 1k to 10 people, getting a 1 month delay on payments requires 10 different deals. If you owe 10k to 1 person, getting a 1 month delay on payments requires 1 deal.
and the psychological boost can be real (victory! instead of a battle of attrition).
And for most human endevours, motivation and psychology is insanely important.
Some people can be motivated by the math of the avalanche, and how they are smarter and doing it optimally than the "easy win of snowball". But often the snowball is pretty damn close to avalanche in costs, and doesn't require fancy tricks to convince yourself you are winning.
On the other hand, an annual 30% interest debt is insanely worse than a 5% interest debt. If the difference is 16% and 15%, go snowball the smaller one -- if the difference is huge, focus on the one that really matters, the big interest one.