Can't see how testing at the border can be any more than a confidence check, the main things are what is the status of the virus transmission in the country coming from or going to, if low prevalence and under control such as NZ to Singapore risk is lower than say someone from the UK where it would be very high risk for Singapore to even contemplate letting free travel without stringent safeguards such as the 14 days quarantine, the capacity to accurately/quickly contract trace and the ability to prevent infected persons from continuing to spread the virus.
So while I can see why airlines want to pursue this as a way to restart more general travel it is also pretty clear why for the most part it is being ignored by governments, especially for those that have actually got control of the situation after initially being burnt as those countries especially would not want to have any work undone by visitors when the rest of the economy is starting to recover.