It doesn't always work to go slower. The speed of least drag is an airspeed, not a ground speed. And commercial jet engines are most efficient around 90% thrust, not at lower settings. So going slower can make you less efficient.
That's also why flying low is really bad for fuel consumption, you're going to have to decrease thrust and you'll be aerodynamically less efficient at the same time.
In general turbine engines are limited mostly by the temperature at the first stage of turbine blades after the combustion stage. It's hard to get reliable instrumentation in this zone so a proxy temperature is often taken from a later stage.
In older airliners there was a table of max ITT values varying with altitude and outside air temperature. In modern FADEC engines the computer does the same calculations. It's not unusual for smaller jets to be set at their max continuous thrust setting shortly after takeoff and be left there until the beginning of the descent. Modern airliners will be flying a cost optimised Mach number.
That Mach number is entered on their flight plan and is used as a basis for ensuring they are separated from other flights on the north Atlantic tracks so they wouldn't be able to change it readily.
The interesting part of all of this is that they would have been assigned an altitude for the crossing, at high altitudes maximum speeds drop (because flutter margins are proportional to velocity rather than effective pressure) but stall speeds increase so the range of viable flying speeds is actually quite limited at cruise altitudes. They probably couldn't have slowed down if they wanted too.
So if you are shooting for miles per pound of fuel, there is a best. You will lose total trip fuel if you throttle up and go faster and you will lose total trip fuel if you throttle down and go slower.
I've only had some college physics and no aeronautical engineering so I could be way off. Of course there are other factors like the amount of lift per unit of velocity and so on...
But you measure speed in this context relative to the air, not the ground.
The fact that the plane is now moving across land much much quicker due to winds aloft is completely irrelevant from an aerodynamics perspective.
The plane doesn’t even “know” that it’s getting there sooner.
This is true of form drag. Airplanes are also subject to a somewhat counterintuitive induced drag that is inversely proportional to airspeed. The minimum total drag is therefore somewhere between a slow speed and a fast speed.
There are three optimal speeds depending on what you're trying to optimize. Maximum range (distance per unit of fuel) is best glide speed, which would be a painfully slow way to get somewhere. Maximum endurance (time per unit of fuel) is roughly max endurance divided by 1.316—even slower. "Optimum cruise," or Carson's speed (max speed per unit of fuel) is roughly max endurance times 1.316.
I'm pretty sure best glide speed times 1.3 can be achieved with less than 90% thrust from the engines of a typical commercial airliner.
https://www.wired.com/2012/10/can-we-build-a-more-efficient-...
It’s still less efficient, but some of that squaring works to your advantage.