Still, I can't accept it.
Enter the admin panel and you will see the tables are broken and/or aligned improperly. Additionally, it seems the header does not contain W3C-valid HTML.
All in all, I don't like the colors. If you follow the "dark" theme, all colors should follow it. In some places, fonts are very difficult to read.
I don't like this idea of replacing it with default one
You don't like, but this is the main concept. This menu doesn't contain only 3 items like by default. When you are logged in, there appear 4 items on the main page. If you are under Topics listing, there are 6 items appears. If you have Private Messages installed, they require a completely new line with more items, because there will appear "New" and "Reminding" indicators. Forums Checker, Polls and many other add-ons require additional menu items.
Don't you think for 8 years we have not thought it carefully? ;-) Everything you see in miniBB, comes not just because it appears so. Every element has its meaning.
Why, in general, should the software have many skins available? Because users could then easily install it, or allow forum members to choose the skin on their own taste. Everything should be simple, without adjusting additional graphics, HTML or other things. Header belongs to the website owners themselves, everything they want to download, is the layout which suits their website best.
How your own images could be involved in that? You need only to create a CSS schema, choosing proper colors and fonts. Then it could be adjusted to many sites. If you have your own graphics, it could be used only for one website, which already has similar graphics. A rare case, no?
It appears that your skin is limited with the basic package only. This is bad. Check the variation of extra-mini skin on demo forums. It uses different fonts, different tables width, different backgrounds - but this is enough for a custom skin, because then you could switch from the one skin to another easily, and it gives a completely new look to the board. Nor header nor any other template should be affected in that process, the idea around CSS is exactly that.
As I know, the best colors for reading for eyesight are black on white.
Your knowledge doesn't comply with mine :-) Black on white comes from the "natural" paper books or newspapers. Sure, when the paper has a white color, the only acceptable color for reading is black.
But monitors, specially LCD monitors, are completely different story. Monitor colors and papers colors are strictly different even if they are printed with the top technology.
On monitor, as more white you will have on the screen, as more it's unpleasant for eyes, because it means the white light lamp will damage your eyes directly. It's the same effect like when you are looking directly into a regular lamp.
As milder background color you will use, as better it is for the eyes, and as it is better for reading...