I completely agree with your math. Paying the minimum payment on an Income-Drive Repayment plan for 20–25 years results in a higher overall repayment and the “tax bomb” upon forgiveness. Paying down the debt ASAP would be the cheapest option.
However, there are many borrowers who simply cannot afford to pay extra. Even the payment on a standard 10-year plan puts them at the financial breaking point. That’s the audience for the particular piece of advice you highlighted.
For these borrowers, and I include myself in this group, they should pursue either a) Public Service Loan Forgiveness (my choice) or b) IDR forgiveness. Either way, the ultimate goal of this strategy is loan forgiveness, so why would you pay anything more than absolutely necessary when someone else will pay it for you later?
Your point about the tax bomb can’t be ignored. However, I would argue that it only strengthens my point. If you can find a way to reduce your monthly payment on an IDR below its current level, then you can just put that money towards a savings account for when the tax bomb does arrive. Whether you actually do that is another question, but it’s a strategy to consider.
Lastly, some borrowers place a higher priority on starting a family or some other long-term goal that they feel cannot or should not wait due to their student loan debt. This advice also applies to them. Even though the source of their decision is personal instead of financial, the impact of this strategy still benefits them.