Is there any way to reduce minimum brightness without root?
Impossible.

I used to have your idea and I gave it a try, but to no avail. I rooted my phone and did the following

echo 1 &gt; brightness


... but it seems to be identical to its lowest value, which is in my case, 20.

The mininum brightness is something in the screen's firmware, which is even beyond the Linux kernel. You can't change it unless you flash a custom firmware to your screen, and it will almost surely destroy it, so don't attempt to do so.