Currently, user could right press on toolbar and select show/hide menu. Why does not go into hamburger menu with more programs? I think developers do not go into hamburger menu, because they just scary user could not use one’s software. Solution is to allow users to fast force to show normal menu and hide it - not every person known he/she can right click on toolbar.
So:
Add small button near hamburger menu button called show/hide normal menu
Currently in Firefox using KDE Discuss - I cannot use a context menu on a toolbar to select show/hide menu - though I can customise that way. I can certainly use the ALT key to make the menu visible (which I assume you’re referring to as the ‘normal menu’) and which I agree, should always be accessible in any software.
Quite often, with KDE software, I have no Hamburger menu visible (I prefer it that way unless a toolbar is absolutely necessary I like it cleaned up).
If I open Kate, I use CtrlM to toggle the menu; which is the same behaviour as in Dolphin.
Overall, I found your post rather confusing and difficult to understand - partly because visible icons and toolbars are not consistent across all kinds of applications I cannot grasp the context here.
I think that in addition to CtrlM , Alt should also work across as many applications as possible, like in Firefox and Thunderbird. The advantage is that the menu then disappears when it loses focus.