(1) storing some or all of the energy required by the firing mechanism to fire a round...
This is a rabbit hole with no bottom. Ok, now you need to define how much energy is required by the firing mechanism to actually fire the round. Who does the survey that accurately defines the amount of energy required to fire all of the common primer types on the market? Who catalogs that information for ease of access? What about calibers which can use more than one type of primer? If one primer requires much more energy to fire, that could potentially change the definition of what double action means in a particular firearm depending on what loading is being used.
Does any of that make the definition of double action clearer or more easily understood? Just the reverse, actually.
Then you have to decide if a design which is over-engineered to store, say, 25% more energy than is "required" in order to absolutely insure reliable ignition is still a double action if the trigger does the work of storing 90% of the energy in that safety margin. It's obviously doing a lot of the work of storing energy but since all of the energy it's storing is actually surplus energy, now by this contrived definition of DA, the gun isn't double action.
So who would understand the concept of a DA trigger better after someone were to theoretically hash all that information out? No one.
A SA trigger only has one function - to release previously stored energy required by the firing mechanism to fire a round.
What about the issue brought up by random_guy? He correctly points out that most firearms with a traditional sear require the SA trigger force to cam the hammer back at least some small amount in the process of "releasing" it. This stores energy in the mainspring (albeit a very small amount) but that's still a function other than simply releasing the energy. Using your argument, unless you can define and precisely quantify this amount, no one will understand what an SA trigger is. Of course that's not true at all. We all understand what an SA trigger is even though the trigger action typically does slightly compress the mainspring some small
unspecified amount in the process of releasing the hammer.
In this case a percentage.
No, this only obfuscates and complicates what is otherwise a very clear and simple concept. Besides, what percentage would you use? Percentage of energy stored in the mainspring? Percentage of compression by length? Percentage of force applied overall? Percentage of firing pin momentum? Why is one better or more descriptive than the other?
Since the concept is already adequately clear, already very clear without a specifically and precisely defined numerical threshold, the definition of such a threshold provides no value added unless there's some need to meet a predefined legal requirement or contractual specification.
That still seems somewhat less than clearly and precisely descriptive.
It is very clear and very descriptive. The fact that it doesn't provide a numerical threshold doesn't cause any problems in terms being able to attain a clear and practical understanding of when a trigger performs cocking action and when it doesn't.
The bottom line is that it is very easy to understand the concept of a double action trigger vs. a single action trigger. It's even easy to understand that there are variants of what are commonly called 'DAO' triggers and how they work. And all of that understanding in no way requires some artificially defined precise numerical threshold. Trying to be extremely precise by making up some arbitrary threshold provides no value added and actually complicates what is otherwise a pretty straightforward topic.
When a definition relies on key words that lack clarity and precision, it is difficult to see how the definition could be consistently understood by multiple readers.
In some limited circumstances that might be true. In most cases it is not just false, a little thought will reveal it is ludicrous.
Let's take a simple example. I suspect that only 1 person out of 100 could accurately define the wavelength ranges that qualify as red light, as yellow light and as green light. I suspect that the specific thresholds of each wavelength range would vary from one source to another given that the spectrum is continuous. And yet in spite of all that lack of precision and conflicting information, there is no confusion at all when people are taught about how to respond to traffic lights. Can you even imagine anyone in a driver's ed class legitimately asking the teacher what he meant by a red light or demanding accurately defined wavelength thresholds for what constitutes various colors of light and legitimately claiming that without such precise definitions there would be no way to know when to stop, go or be cautious? Of course not.
What about someone claiming that they can't respond to a yellow light properly unless there's a legally defined precise threshold for how much they should slow down or how cautious they should be? It would be ridiculous. People have no problem understanding how to respond to a yellow light even though there's no precisely defined standard of caution to employ.