$e$ is only defined by the fine structure constant if you choose it to be. But that's not the choice the SI made.

What choice did SI make?

``An exact expression for the unit ampere in terms of the defining constant 𝑒 is 1𝐴=𝑒/1.602176634×10−19 '' $e$ is the defining constant. It's not defined by something else.

That quote is in my answer. Their full statement is that $e$ is defined in terms of A, and A is defined in terms of $e$. That's why I mentioned the lawyer. Read on somewhere to see how $\epsilon_0$ is defined (or in my answer). Are you saying $e$ is not a number?

It's a defined number, just like $c$ is.

In a sense, you are right. SI has defined $e$ as a fixed defined number. But to do so, it has had to redefine $\epsilon_0$ and $\mu_0$ as experimental results, because of the equation I wrote for $\alpha$. $e$ was an experimental number before 2019.

Indeed that's what they did. Choosing which constants are defined, which are derived, and which are to be measured is part of the game.

This game has changed almost every number in EM.

Every instrument I've designed using them still works, and I haven't had to retract a single publication.

The SI number for $\alpha$ is 0.0072973525693(11), so it wouldn't affect anything you do unless you require supreme accuracy (which some experiments require).

I make that point at the end of my answer. For most people, the uncertainty introduced is only conceptual, but I think it is a step backwards.

Alpha is a dimensionless measured quantity, so it's the same in any consistent unit system. Changes to the SI have no effect.

I've never heard of someone being anti-2019 SI unit redefinition.

You have correctly pointed out that mu0 used to have a definitional value, and now it has a measured value that can change with time. but do you understand that this will always be true for something in any system?

you make it sound like this is a "bad" thing, but the whole point of the 2019 redefintion is that it's less bad than the previous definition. In the previous definition, mu0 had a fixed value, which meant that the ampere was "whatever amount of current exerts this particular force," and since the coulomb was 1 amp times one second, the coulomb was "whatever amount of charge is exchanged by the current which exerts a certain force".

So the definition of the coulomb was subject to change over time as measurements of this current, and the resulting charge, became more precise

Now, the coulomb is a fixed amount of charge in terms of a certain number of electrons, and mu0 is what changes with improved measurements. The whole point is to choose which things to define and which things to measure based on which measurements are most precise to minimize how much our values change over time

The meter is now defined exactly with no change due to any new measurement. It is defined by the equation: distance equals speed times time. Before 2019, the ampere was defined exactly with no change due to any measurement in terms of the newton and the meter, with no change due to any new measurement. It was just a more complicated equation. The definition of the ampere and the Coulomb did not depend on any measurement, just as the meter no longer depends on any measurement.