If I understand correctly, your argument is: We know in general that magical light illuminates, so unless a darkening effect makes a specific exception, the light should function as stated.
It seems to me like the reverse argument works just as well: We know in general that magical darkness darkens, so unless a light effect makes a specific exception, the darkness should function as stated.
Which is exactly what happens. Darkness (the spell) describes how the darkness it creates is different from "normal" darkness. Each light source does, in fact, tell us how it does work. Each light source explicitly has a range with the effect listed. Unless there's a light source, there's darkness. However, Darkness is a specific exception on normal darkness. The specific of each exception are usually stated on the exception itself: Darkness has to deal with how Darkness works: "It creates an area of magical darkness: that's how it is magical".
If the darkness spell only said "... magical light can't illuminate it," then I would probably agree with you; a spell does what it says and what that says is that it suppresses non-magical light. But in fact the first line of the spell says "Magical darkness spreads ..." That seems to carry at least as much descriptive weight as, say, continual flame's description "a flame, equivalent in brightness to a torch, springs forth ..."
And it does spread: it has a specific pattern that is, again, different from how normal darkness works. It is another difference from the normal state of darkness, an exception on the specific: it spreads from one point in space and can be blocked by being completely enclosed by opaque objects. It specifically does NOT interact with magical light sources unless otherwise stated (spells of low level).
What you are trying to argue is that in absence of directions, there's no way to determine. However directions are there: how darkness works and how light works and the fact that 5e is an exception base system that works on specifics beating general and general applying where specifics are missing.
Does light illuminate darkness? Yes, unless said darkness has some proprieties that make such darkness so that it can't be illuminated. Darkness does so, only for non-magical lights. It also prevents magical lights from spells of certain kinds from illuminating the area by dispelling them. That's the extent of the specifics.
You are not working in a vacuum. You are not trying to prove "existence". You are working on an exception based system where generic is beaten by specific and is applied where specific is not there.
You are assuming dakness, applying specifics from light and Darkness. If the two are in conflict, the more "specific" one has precedence (Darkness, in this case, calling specifically non-magical lights+spells). Otherwise, you apply general. General is: darkness, unless light.
I might have gone overboard with repetition

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