Can't pass theme changes to children nodes

In theory I should be able to change font, textures, etc. of any control node (buttons, panels, and others) if I place all of them under a unifying parent control node and add a unique theme to that parent. However, it doesn't really work for me. See the pic.

Main has the theme set in the Inspector. It has a new global font and changed textures for buttons and panels.
Green - font and texture got changed
Yellow - changed partially (in case of Panel, the font is changed, but not the texture)
Red - no font changes
For now, I've got only two things to change: fonts and textures. And if textures 'mostly' work (I can't get Panel textures to change), font is more problematic.

So, basically buttons get changed in textures, but not panels. Only option buttons and panels get changed fonts, but not normal buttons.

What am I doing wrong?

For those with the similar problem in the future: if you are setting a global change for a theme and you want it to be visible in all affected elements, check if you have not accidentally set something specific for a specific element.

In other words, if a button has a set font, it will not use the default font you set for the theme.

In even otherier words, go to the Theme editor, chose the object you're editing, Fonts, and click the Delete button you see there (if it is there) to use the fonts you set as default for the whole theme.