RFID wristband for cashless payments
Why do RFID wristbands used for cashless payments use HF over LF
  transponders?


There was an easy migration path from contact based chip-cards to HF contactless. On the application level some of the HF tags support the same ISO7816-4 protocol that the chip based credit-cards understand. 

For LF tags no such simple update was possible. That's why HF was the natural choice.


  Would I be right in understanding that for cashless payments using
  RFID wristbands, I should be looking at ISO14443 compliant tags.


Yes, if you want to interact with existing point-of-sales terminals you're pretty forced to use ISO14443-A and ISO14443-B tags. If you roll your own payment terminals you have more choices.


  Is a double-tap unavoidable?


No, it is an implementation detail of this technology. You don't need to double-tap if you use contactless credit cards for example.