You only get a single tax deduction, not a double deduction. If you put in $1K and also get $0.1K gains in your HSA, for example, you only get a total of $1.1K tax deduction. There is no "triple tax benefit".
The point is you never pay tax on that money.
1. Your contribution is pre-tax
2. Your growth is tax free
3. Your withdrawal is tax free as long as you have receipts for qualified expenses.
I personally don’t have an HSA because it seems like a hassle and I don’t want a HDHP but I can see the appeal.
My point is that it is far from a "rare triple unicorn" or whatever overhyped language they use. You can put money in an IRA, get a tax deduction, and then not pay tax on the money and the earnings if you take it out via a QCD (qualified charitable distribution)), but no one calls this a rare triple unicorn. Also, many items paid through your employer, such as health insurance, flexible spending accounts, dependent care accounts also are tax free when contributed to and not taxed later if used for intended purposes. It is just a single tax benefit, not a "triple" tax benefit.