Sure, but this is the internal "copy mode" of tmux, and is not useful to copy text in and out of your terminal.
In most terminal emulators you can also use Shift (or sometimes a different modifier) to bypass application mouse mode and have the terminal emulator handle the mouse event. Of course you can't copy out of the history with this, but that is another limitation of terminal emulators.
This seems more an excuse than a cause. When the "mouse mode" of tmux is off, the copy-paste mechanism works perfectly. There is no reason why this couldn't still be the case when the mouse mode is on. For example, tmux could enable the mouse only for scrolling and resizing the panes, while keeping the correct copy paste behavior intact. But it chooses not to.
Or you could read it with `xclip`, `xsel` or `pbpaste`, something like:
bind -n MouseDown2Pane run "pbpaste|tmux loadb -" \; pasteb
Tagline from GitHub:
> Tmux plugin for copying to system clipboard
https://github.com/tmux-plugins/tmux-yank
I could understand if you don't like tmux for other reasons (being a heavy mouse-user for example), that makes perfect sense. It's not for everyone. But if you take some time to understand why some things don't work like you expect it to (like what's the difference between a terminal emulator and tmux, what they have access to and so on) and how you could solve them, you'd avoid the issues you're describing.
But again, tmux is a tool aimed for keyboard users, not mouse. This tool doesn't fit everyone, and that's ok too. If you're willing to try it, you need to understand a few things before it'll work as you expect, otherwise your expectations will be wrong.
I love tmux and I'm primarily a keyboard user. But sometimes I like to copy a short string from one window to another. Does tmux-yank allow you to middle-click paste on a tmux window? does it allow to select to copy?
For the "select to copy", all the information you need is in the GitHub repository previously linked. Here it is again: https://github.com/tmux-plugins/tmux-yank The specific section you're looking for is here: https://github.com/tmux-plugins/tmux-yank#mouse-support
It's simple for you to try it out as well, have a read about tmux plugins and you'll be up and running in a yiffy.
Also take some time to read up on terminal emulators, shells and what tmux is, as you seem to hold slightly off assumptions around where the problems you're experiencing are actually coming from. The reading and understanding will only make your personal knowledge base larger and deeper :)
To get pasting from the system clipboard, you need something like https://github.com/brennanfee/tmux-paste It will copy whatever's on the system clipboard into tmux's paste buffer, and paste it, all with a single middle-click.
I've only recently started using tmux, and all this clipboard stuff was the biggest stumbling block. But I think I've got things work well enough now.
tmux-yank copies whatever you selected to the system clipboard (xclip, clip.exe, etc.)