The primary reason for the existence of these programs is to stop people being refused entry at the border and having to be deported.

For example, I'm going to presume you're a US Citizens. Previously, US Citizens could enter Australia without a visa - however only if they met certain criteria such as not having a criminal record (that's over-simplifying, but close enough). If someone with such a record turned up at the airport, the airline would let them board because they had a US passport, and US citizens are allowed enter Australia. On arrival in Australia they would be taken aside as a result of the answers on their incoming passenger card, interviewed, and likely deported and put back on a flight to the US as they were not eligible to enter the country. Obviously this isn't a good situation for anyone, including the passenger.

With a pre-approval program, this doesn't happen - or at least, the incidence of it happening is significantly reduced. The ineligibility is detected during the application process, and the ETA is not issued. As a result, the passenger cant board the flight, and never needs to be deported. It also gives the country additional time to carry out checks on passengers in advance of them arriving.

For most/all of these programs, the fee is intended only to cover the cost of the program. In fact, the Australia ETA is actually "free", but there is a $20 fee that goes to the company that runs the systems behind it. Prior to Covid, travel agents and airlines could apply for ETAs at zero cost. (The NZ one is a bit of an exception here - they add on an extra visit fee as a part of the NZeTA application, but not for citizens of all countries).

The "E" in ETA stands for "Electronic". At check-in, your details will be sent to the Australian Government, and they will tell the airline weather you're approved to board the flight or not, based on your ETA/Visa/etc status. If you hadn't had an ETA, you would have been denied boarding.

I hit this a few weeks ago travelling to Canada. I'm a US Permanent Resident so as of last year I don't need an Canadian ETA, however United's app-based check-in doesn't handle that fact, so my check-in failed stating I didn't have a valid Visa/ETA. I applied for the Canadian ETA, was approved a few minutes later, and then tried to check-in again and this time it succeeded. The only way United could have known that is by checking with the Canadian government, which is exactly what happens!