In many cases, they are. That's certainly the trend, to make it easier on the passenger. Plus, it makes it more of a "hidden" tax that most people won't realize they are paying. In the last 10-15 years, both HKG and NRT have switched from the "pay in cash upon departure" method to the "collected by the airline as part of the ticket" method.

As to why it was ever collected in cash, well, it's just a simpler system to administer: all you need is a person before the security checkpoint to collect the cash, or alternatively a vending machine to collect the cash and dispense a ticket and then a ticket-taker before security. That's far easier than liaising with every airline to count passengers and collect the fee.