Sorry, but that is just not realistic. The roster that I always used to struggle with was a late night check in to fly from Heathrow to JFK. I can't remember the exact report time but it was around 18:30pm with a departure at just after 20:00. Scheduled block was around 8 hours which put you landing into a very busy JFK environment often in crappy weather at around 04:00 body time.
Now, this was a two crew operation so no chance for inflight rest in the bunks and often would be the first duty on the roster after days off. I don't care who you are but it is almost impossible to prepare for a duty like this so that you can do the whole sector without feeling bloody shattered at some point during the night given that you have probably only had 2-3 days at home after potentially just come back from somewhere East. Controlled rest was and is the only sensible solution.
We are digressing a little bit here as controlled rest is NOT a tool for fatigue, it is a tool to use to combat tiredness that occurs when you are flying while your body is saying sleep. If you are fatigued you should NOT be at work, if you are tired you should grab the opportunity to rest whenever you have the opportunity as allowed by you company SOP's. This tiredness will happen in any job where you are expected to work through the night, the only way that FTL's could get rid of this kind of tiredness would be to BAN all flying between the hours of 23:00 and 0600. It ain't going to happen.