There's apparently a ZSH plugin for this with a quite a few stars, though I haven't used it and can't speak for how well it works. In other shells what you want just doesn't exist to my knowledge, though it should be possible to script it with enough effort.

The problem is that in the terminal you always have at least two layers of input handling in the terminal emulator and the shell. And these layers talk to each other by emulating a 70s VT100. This leads to some issues, in no particular order:

• Terminal emulator keybindings will step on shell keybindings, and the shell will never know about it because it can't actually see the keys being pressed.
• Even if the terminal doesn't care about a key, it might be impossible or error-prone to detect anyway. This applies to surprisingly regular keys like Tab.
• As you've noticed some terminals try to get clever and do things like making Ctrl-C copy if you've selected text. The shell doesn't know about this either.
• Most shells and TUI apps have selection modes. These are independent from terminal selections.
• There's no standard way of using the clipboard in Linux, but multiple different ones that may or may not work.

All of these problems gets worse if you add multiplexers like tmux by the way.

Now it would be possible to write a bespoke terminal emulator and shell combination that unifies selection and makes all the reasonable keybindings actually work. There are attempts at this, such as the Emacs Eshell. Unfortunately Emacs people don't quite share your idea of what reasonable keybindings look like (and it's also a little bit broken, though for mostly unrelated reason).

Ultimately though the main reason this is an unsolved problem is that most Linux users just get used to the regular Readline line editor that all commonly used shells ship with. Complex edits can always be done in your $EDITOR (via C-X C-E in Bash).