The first is a human psychology hack -- paying off small loans so you can feel the results and be motivated to keep at it. You're right, it is costly to ignore a higher-interest loan while aggressively paying off a lower interest loan... but it's much more costly to lose your motivation and not pay off any of the loans. (For someone with the discipline and motivation to pay them off without this hack, I agree, pay off the highest interest rate first.)
The second hack is the "snowball" idea -- once loan A is paid off, use the cash flow to pay off loan B, and then use the cash flow from A and B to pay off loan C. This works no matter which loan you pay off first. As a followup, once most or all of the debts are paid off, I recommend using some of the freed-up cash flow to increase savings rate.
The first is a human psychology hack -- paying off small loans so you can feel the results and be motivated to keep at it. You're right, it is costly to ignore a higher-interest loan while aggressively paying off a lower interest loan... but it's much more costly to lose your motivation and not pay off any of the loans. (For someone with the discipline and motivation to pay them off without this hack, I agree, pay off the highest interest rate first.)
The second hack is the "snowball" idea -- once loan A is paid off, use the cash flow to pay off loan B, and then use the cash flow from A and B to pay off loan C. This works no matter which loan you pay off first. As a followup, once most or all of the debts are paid off, I recommend using some of the freed-up cash flow to increase savings rate.