If a monitor has bad contrast and you turn up the brightness, that's not the fault of the light source. That monitor still won't even come close to the amount of blue light that a blue sky emits, even at maximum brightness.
Personally, I think all monitors made in the last 10 years should be as legible at low brightness as a piece of paper is in an equally poorly lit room.
On the other hand, passive displays (books, e-ink) by their nature inherently match ambient lighting conditions, because they simply reflect ambient light. This is the equivalent of a monitor with a much wider range of contrast and brightness levels equipped with an automatic adaptive adjustment with sub-nanosecond response times, something that simply does not exist with present technology.
So yes, in theory a monitor could potentially match a passive display in terms of reducing eye strain and tiredness but in practice it is beyond the state of the art for now.