The important question is how much energy do they need to put in to get the result. The goal can be machined aluminum or car at destination. For lots of processes, the output energy, like moving car or shining light, is important and the goal. Higher efficiency means can put in less energy and get the same result.

Light ends up as heat, but LEDs are more efficient cause they don’t produce extra heat. Electric motors are more efficient than combustion ones so electric cars end up going farther for same input.

Sure, it is reasoably easy to say that A is more efficient than B, and even quantify how much energy A saves in comparison to B. But that is only a relative measure; it is far less obvious how you'd quantify the waste in absolute terms like the chart in question here seems to do? To do so you'd need to know some theoretical ideal minimum energy process that would get some equivalent end result as a reference point, but that seems wildly infeasible to estimate

In your example of machining the useful energy consumed was in the kinetic energy transferred by the motor into the bit. The noise and heat and other forms of energy dissipation that didn’t go directly into machining the object were wasted or lost. If your goal is the machined part, any energy that wasn’t directly necessary or if it’s expenditure were zero and the part would have been machined identically, is considered a waste or lost energy. The “lost” doesn’t mean the rest of the energy were somehow captured or retained, but that it was captured productively towards some goal. Perhaps the term is confusing or misleading, but that’s what it’s intended meaning is.

> the useful energy consumed was in the kinetic energy transferred by the motor into the bit.

This doesn't solve the problem, because the final machined part is not moving, and thus has no kinetic energy.

In order to get an efficiency number, we would have to know what 100% means. Maybe it's possible to calculate the minimum energy required to break the chemical bonds spanning a given cross sectional area of solid aluminum?

I imagine that you could (very theoretically) recover this energy by cold welding the aluminum back together a vacuum.

Right but it’s not a maximizing theoretical loss function, it’s picking a specific expenditure of energy as the goal - kinetic energy of the bit. Particularly you don’t know the goal of the bits motion, and the work the energy does could translate into the machined parts final configuration or something else. The goal isn’t specially to account for energy in some full final system but to give an optimization function for the tool itself to maximize. You’re looking at it from a physics point of view rather than an engineering point of view, the engineering view is practical - how much energy is expended to get a certain amount of work done by the bit and not doing other stuff like heating the environment, making noises, inducing vibration. The metric is a practical one, and it’s never meant to capture the entire energy transfer dynamic in a physics sense.

It's not about energy capture. It's about energy being used to accomplish useful work vs energy expelled towards non-productive ends. And I fail to see how this is a useless measurement of energy consumption when it's the entire reason we harness energy beyond what we can consume by eating.