It appears that a 734 is great for phx to hnl. Doesn't mean it's the correct plane just because it has range and demand. Many times these planes are used when they couldn't have been legally.
The 757 was designed to replace the 727 on higher demand domestic routes. Because some airlines bastardized them over the past few years for these routes doesn't mean that was the original design for this plane. The 57 was cancelled because the 739 carries almost the same number of pax.
The fact remains that the 757, regardless of what it was designed for and whether you agree with it personally, has found a successful niche as a longhaul aircraft for thin routes. It should be possible to replicate this in AWS. I am not talking about LHR-JFK and the like, but specifically low demand routes which cannot support a wide body.
And I reiterate how major airports would require airlines to fly appropriate aircraft.
I cannot comment on the US, or other parts of the World, but in Europe that is certainly not the case. An airport may urge, persuade and encourage the use of larger aircraft on certain routes, but they cannot insist in it. And if they did, many existing routes would be cancelled which is neither beneficial for the airlines, the airports or the passengers.
If the owners of MAN insisted that United use a 767 rather than a 757 on their route from EWR then United would most likely ditch the route altogether. Same could be said for many other routes.
Even LHR cannot require or insist that an airline uses a certain type of aircraft. If the airline has a slot, they can use whatever aircraft they want to make use of it.