Of course an experienced Exalt who bothers to measure such things will have a rough idea of when their anima flares, or how long they can keep up a certain level of activity.
Just like I have a rough idea of how long I can run at a certain speed, and when physical activity will start to cause me pain.
That does not, in any way, translate into said Exalt knowing anything about motes.
Why?
Because it's not an easy formula that is constant at all times.
In 2E, you have mote regeneration by stunts. In other words, sometimes you just happen to have more motes than expected - and you can't exactly differentiate that from your charms using less motes, for example.
In general, because you're not privy to your dice rolls. Sometimes, you can jump a distance of X without using any charms, so it takes no motes (lucky roll). Other times, you have to use an excellency, or another charm, so it does take motes. And that gets even more complicated with dice pool modifiers (which can happen at any time, arbitrarily depending on the storyteller and stunts) and especially once you're targeting others (because you won't know their defense values).
So in other words, you can't even measure performance exactly.
Just like in real life - despite sport sciences being a thing, an athletes performance is still not 100% predictable.
And an Exalts charms are
not buttons to be pushed at-will by the Exalt, divorced from any activity!
An Exalt doesn't go "okay, I'll use my First Ability Excellency five times, spending three motes each time". Not even if you replace the words and instead say "Okay, I'll use the Suns Blessing on this activity five times, at moderate strength".
Instead, you'll get this: "I try to do this", "I try to do this harder" and "I try to do this as hard as I can". Just like you would say "okay, I jog a bit", "I start to sprint" and "I run as hard as I can". Or "I'm writing my thoughts down", "I'm structuring my post properly" or "I'm thinking really hard about this before posting it, and construct it carefully". The latter of those would certainly activate charms for an Exalt, but it's not a conscious choice to do so in-game.
Incidentally, this also means that an Exalt who's not using all available charms on an activity is holding back in-universe. An athletics-focused Solar who's not running faster than a race horse is consciously holding back, just like you would if you're riding a bike at a slow pace because you're driving alongside someone slower.
Yes, those activities could be performed in a lab. That would give your results about the Solars performance, and you'd see that if they exert themselves they do produce anima flare and such, and eventually run out of energy. Which is pretty much the same result we today get from sport sciences and measuring athletic performance.
Except Charms and motes are about more than just athletic performance, or other easily-measurable thing. How do you measure a Linguistics Excellency? A Lore Excelly, a Sail Excellency? Never mind more complicated charms.
So you can't even measure the whole of an Exalts abilities, and any picture you'll get will be quite incomplete.
But that's not what prevents you from figuring out motes.
What prevents you from figuring out motes is that you're only measuring performance. Measuring an athletes performance tells you nothing about cell metabolism, mitochondria activity, osmosis and so on, right? Never mind about the underlying chemistry, or the physics underneath that. Just measuring an electric charge going through a nerve is really hard.
Well, for the same reason measuring an Exalts performance won't tell you anything about motes.
To measure motes, you would have to look at the physics of them. Which needs really sophisticated equipment, and underlying theories to even attempt. Equipment and knowledge that does not exist in the Second Age.
Motonic Science was comparable to quantum science for a reason - it needed really advanced, expensive research programs to actually observe (instead of just writing theories). And a single Solar - or even a circle of them - won't be building the Exalted equivalent of CERN and the LHC. Because they won't even have the tools needed to build the tools needed to build the tools - or even the theory to conceive the idea for the tools they'd need!
Sure, Benjamin Franklin could measure an electric charge. That doesn't mean he could do so in real time inside a living human being. Or that he could have built equipment to measure electron volts, and observe how charge originates from quarks and leptons. Likewise, your second age solar won't actually work with motes, and at best have a rough and inaccurate (=not matching ooc rule-measurement motes) idea of "motonic energy".
