For the next revision: remove the mole from the SI. It's completely pointless. A number is not a unit!
Instead replace it by the bit, the fundamental unit of information.
It seems that the reason is that chemists don't care how many atoms there are in their reactions. It would be inconvenient: fractions of atoms don't make sense, and the numbers are far from human scale. They just want an agreement, so that even if they don't know the exact number of atoms in their test tube, they know they all have the same number. That's what units are for.
The definition of units are done in the most convenient and precise way possible. And they are updated as science progresses. For the kg, the artifact used to be the best we had, alternative methods weren't precise enough, they changed that to the Kibble balance because now, it is better. It may change again at a later time if we find something better.
Back to the mole, it used to be defined as the ratio between the kilogram and the mass of a 12C atom because it is the best we had. Now that we can count atoms with more precision, we decided to change it to just the Avogadro constant, which becomes fixed. Again it might change. What may happen (or may have happened, see Avogadro project) is that we can define the kilogram using the mole, making it fundamental.
testing my scale with a mirror that contains a kg of photons doesn't sound very convenient.
I get the feeling this just changes the definition of "Kg", but not how reference Kg's are actually produced?
The standard changed because people came out with a apparatus for using it. If there wasn't one, it wouldn't have changed.
But it's fit for measuring micrograms up to grams. One won't measure actual kg on it, at least not currently.
The difficulty with this simplistic view is that it turns out that nucleons actually differ in mass slightly, depending on which nucleus they're in (and, also, isotopic ratios matter), which means there are a few different definitions you can use for the number of nucleons in 1 gram of stuff. In practice, the difference is small enough that it doesn't matter for most uses, especially if you build it into your table of atomic weights.
If we identify the entropy formula
S = kB ln W
Related to this is the fact that the Avogadro constant, 6.02214076×10^23 mol^-1, is equal to 1.
The mole is just a unitless number which isn't used for many definitions, while the bit (or preferably, Shannon) has a fundamental use in information theory and the wider field of physics.
The mole is a human specific number, the bit is a property of the universe. Information is a physical quantity, just like mass or length, and deserves to have a unit in the SI system. You could use other bases, like the nebit (natural log) or Hart (base 10), but bit is most elegant as it uses the smallest integer base possible, 2.
https://en.wikipedia.org/wiki/Parts-per_notation#Uno
However, I don't entirely disagree with where you go with this, but in my opinion, one ought to:
1. Use the nat an normalize everything else (which might seem like an odd idea at first, but think about it):
https://en.wikipedia.org/wiki/Nat_%28unit%29
But, if we assume you want to avoid the normalization, then it would seem more sensible, due to numerical efficiency, to use balanced ternary, which actually has, unlike what people who rather cluelessly apply the literal textbook (and terrible) metric of 'Radix efficiency'(an entirely artificial measure originally invented to account for engineering concerns related to vacuum tube spacing.) would presume, higher numeric efficiency than unsigned ternary, as shown here by a then Indian computer science student, Abhijit Bhattacharjee, whose work on this unfortunately only remains accessible via the Internet Archive Wayback Machine:
https://web.archive.org/web/20090312094241/http://abhijit.in...
He actually got a reply by Marvin Minsky(to an email he had sent him) at some point (also available via archive.org, but only if you do a lot of trickery which I can't do from my mobile phone, I've however previously verified the quote he provided on the bottom of the page and it does, by all things I could account for, indeed seem genuine), which I'll quote here:
"Yes it is a fascinating subject, and your explorations and descriptions are extremely readable. I hope it gets the interest of more mathematicians."