As is so sadly lacking in so much of the approach to controlling and living with covid, this is a lack of pragmatic systemic policy. Of course, a fully observed two week whole household quarantine, direct to home, no going out, etc is going to be most effective at control, infact why not permanently lock away the entire population and to hell with the economy, and all the degradation and loss of YOUNG lives that brings? Whether the quarantine is 14, 10 or 7 days, most people can't extend their time off work (and life in general) for this long.
the reality is that observance of the quarantine is going to be very low, maybe less than 50%, which makes the test and trace equally effective, even if one assumes the (rather pessimistic) reliability % in the post above. Even if it is slightly less effective, it's a mitigation measure against spread, amongst all the others (masks, distancing etc, that everyone now does). Testing also has the advantage, that it doesn't destroy the airline industry, and provides confidence in booking. Austria uses it. The other far more sensible approach currently not used, is to only quarantine flights from high infection areas.