They don't work everywhere though, making them basically useless. For example ctrl+a and ctrl+e don't work in the Safari address bar or the text box I'm typing this comment in, or TextEdit, and many other native text widgets.
If, however, you desire more control, you can use Karabiner-Elements [0] and one of the many [1] community made emacs-like configurations to have this behaviour system wide, these also add many many more keybinds (such as C-w to delete last word) to further emacsify your workflow!
1. karabiner-elements.pqrs.org
You must have broken a configuration or have some other problem. I'm writing this in safari and can use these bindings in this text box and the address bar right now.
(FWIW, I just tried this in TextEdit's plaintext mode on Big Sur and it does indeed work - more than likely due to the UNIX heritage, the emacs bindings work here too)
It is well known that Command-L will focus the address bar and select any text that might be there, so overriding it is generally a bad idea if you can avoid it.
The same goes for 3rd parties - my Dad is a recent convert to macOS and is frequently stumped when Control-A doesn't select text in Microsoft Word - I explained this to him, but in the moment he sometimes forgets.
The biggest and best thing about MacOS shortcuts is that they don't stomp over typing ASCII controls.
1. Type a sentence in TextEdit
2. Ctrl-A will go to the beginning of the line
3. Ctrl-E moves the cursor to the end
It's a native app, and will dutifully select all text with Command-A - but the other keys still do something. A paradox, to be sure.
I do blame Microsoft for the confusion I described, but I'm not sure there's a way they can solve it among their Mac customers without doing as you mentioned and making someone else's life difficult.
If a mac app has mapped ctrl+a to select-all, this should not be called "working." It is an abomination and should be purged from the universe hastily and with extreme prejudice before the cancer spreads.
I understand and sympathize with the difficulty of moving between ctrl/cmd as super keys, but there are a hundred shortcuts with the same problem and forcing mac to adopt the poor keyboard choices of windows is not the answer.
The proliferation of many smaller writing apps (iAWriter, Byword, 1Writer, and on and on) on macOS means that many of these people probably could leave Word if they tried or switch to a plaintext app which can give you a styled preview (ahem, BBEdit) and they would be fine. Almost all of the features are there.
It's just the comfort of Word as a known thing and the idea of how people use computers to create text which prevents them from taking that leap of faith.
Fortunately it's not just 3rd party writing apps that behave correctly. Pages, Keynote, even Google Docs all have the correct behavior.