In this question, the first answer (though I don't completely understand that answer) states that $\epsilon_0$ is the proportionality constant in Gauss' law. If that's the case why isn't it assumed to be just "1". This actually leads to the question, how was $\mathbf{\epsilon_0}$ measured and determined, which again beings me back to "What is vacuum permitivity?"
P.S: I made a series of questions, here. But as it was too broad, I was told to form separate questions, but I have linked everything there, in the comments, kindly take a look.
Answer
As the comment by G. Smith says, you can actually set the proportionality constant to one. But then you would have to measure electric charge in some other units.
Consider the setup of SI units. One coulomb is the charge that is carried by a current of 1 Ampere in one second. An Ampere is defined as the current that causes two infinitely long and thin wires at 1 meter from each other to attract with a force of $2 \cdot 10^{-7}$ Newtons per each meter of the length of the wires. So, this definition is kind of tied to the Lorentz force. When you ask a question like "What is the Coulomb force between two static charges in vacuum?", you get a strange constant.
In the Gaussian units, for example, the situation is different. Here the charge in such a way that the constant in Coulomb's law is equal to one.
In short, if you define the charge so that it "makes sense" in terms of meters, kilograms, and Newtons, you will get odd-looking constants in electromagnetic laws. But if you define the charge units so that electromagnetic laws look nice, then one unit of charge in this system will have an odd-looking proportionality constant to the Coulombs (1 CGS charge unit $ \approx 3.33564×10^{−10}$ C).
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