Some statistics.

But how can we accurately calculate the coefficients then?

The coefficients directly depend on the players' strength. This is a fact. The question is how this dependence is calculated (linear or non-linear) and what it is based on.

It's just my opinion, but because the rating itself is subjective, the coefficients will also be subjective. Or these coefficients need to be artificially set manually, but how? Based on what, if not the rating? Just based on someone's personal preference for one player over another? That would already be subjective.
And 0.80, 0.82, etc., in my opinion, don't guarantee greater accuracy. Although, if we assume that the rating is 100% correct, then it will be something like an average.

Exactly! And no rating can give a 100% guarantee of accuracy. Only variations of +/-. At the moment, we have nothing but the rating table, so that's what we're talking about. Well, the coefficients can be not 0.80, 0.82, but, for example, from 0.5 to 1.5 or something else. They should be derived empirically, based on the analysis of the data obtained with different coefficients.

To understand the meaning of all this, here's another example, exaggerated, for better understanding.

Let's say a Strong Player played against a Weak Player 100 games as Swamp against Rampart, and won all 100 times. Does this mean that Swamp is stronger than Rampart? Not at all. That's why coefficients are needed.

And now, something to think about. Let's say Player 1 played against Player 2 - 100 games as Swamp against Rampart, and won all 100 times. Does this mean that Swamp is stronger than Rampart? Or that Player 1 is stronger than Player 2? It's impossible to say for sure, because... :)