The problem is, there are two conceptions of the back button, and the browser only implements one.
One conception is "take me back to the previous screen I was on", one is "take me one level up the hierarchy." They're often but not always the same.
Mac Finder is a perfect example of a program correctly implementing the two. If you're deep in some folder and then press cmd+win+l to go to ~/Downloads, cmd+up will get you to ~/, but cmd+[ will get you back to where you were before, even if this was deep in some network drive, nowhere near ~.
I feel like mobile OSes lean towards "one level up" as the default behavior, while traditional desktop OSes lean more towards tracking your exact path and letting you go back.
> The problem is, there are two conceptions of the back button, and the browser only implements one.
In web browsers, there is only one concept.
There is no concept of "up one level in the heirarchy". If you want that make your own button in your website.
> one is "take me one level up the hierarchy." They're often but not always the same.
Who expects this behavior? It doesn't make sense. You just want to go back where you were. Most file browsers I've used wanting to implement going up a level in hierarchy, have an arrow pointing up.
If you reached point B from point A - and you tell someone "I would like to go back", then you are expecting to go back to A. Not some intermediate, arbitrarily chosen point C.
You're describing 2 different concepts, back and up, not 2 backs
Desktop had this solved, on Windows there was and remains a distinction between "back" (history) and "up" (navigation).
Browsers actually used to have hierarchical navigation support, with buttons and all, back in the age of dinosaurs - all one had to do is to set up some meta tags in HTML head section to tell which URL is "prev"/"next"/"up". Alas, this has proven too difficult for web developers, who eventually even forgot web was meant for documents at all, and at some point browsers just hid/removed those buttons since no one was using them anyway.
The "Back" remains, and as 'Arainach wrote, it's only one concept and it's not, and never has been "up one level in the hierarchy".
EDIT:
The accepted/expected standard way for "take me up one level in hierarchy" on the web is for the page itself to display the hierarchy e.g. as breadcrumbs. The standard way to go to top level of the page is through a clickable logo of the page/brand. Neither of those need, or should, involve changing behavior of browser controls.