To be fair, the idea of limiting everyone to a certain speed just doesn’t seem justifiable. It’s really hard to limit everyone to say…Mach 0.80, because of the fact that different aircraft cruise at different speeds and that people sometimes need to get to their destinations faster. I just see this as an unnecesssary hassle, due to its complexity.
However, something I could see is being able to have clearance delivery assign altitudes prior to departure (which is an idea that a lot of IFATC members would love to see, feature request linked below), allowing for proper separation even before aircraft reach the oceanic track. I could also see center being able to fix these issues; however, like you said, most people are away from their devices whilst flying these transoceanic flights.
In all, it’s really no big deal if both parties are asleep. The ATC Manual defines these issues as accidental, and no one is at fault. However, if you are indeed at your device, be the bigger pilot in the situation. Little things can go big ways :)