EATs are a throwback to procedural approach control.
At my place we have published (to us) elasped times it takes to complete each published approach. Operating procedurally, first aircraft gets 'no delay', second aircraft gets, very simply, an EAT based on the estimate for the beacon of the first aircraft plus the time it should take to make the approach. Third aircraft gets EAT for the second plus the time interval...and so on...
In the old days, pilots used to adjust their speed to arrive at the beacon at their EAT so hopefully they could go straight outbound...now I am showing my age !!