What speed to fly is like asking how long a piece of string is? Assuming you are in a twin engine aircraft. Many factors come into play,
If you have a short distance to go do you want to be flying at LRC then having to hold because you still haven't completed all of your approach preparations.
As for ETOPS, your company through the regulatory authority will have approved you to a certain time limit, using this time limit a maximum diversion distance will be calculated (under EASA, isa, nil wind etc etc). Assuming the worst happens and an engine failure occurs at the ETP (which coincides to be at the maximum diversion distance) you may exceed (legally) your ETOPS time limit due to actual winds, not flying the diversion speed as defined in your operations manual etc.