AUCTeX provides the feature to wrap opening and closing inline equation markers around active region on pressing $, when TeX-electric-math is non-nil (and this isn't the default). In order to have this, the delete-selection property had to be removed. Actually, its behavior can be dynamically determined by a function, so that
(put 'TeX-insert-dollar '...
I've argued the same thing for a long time: delete-selection-mode should be turned on by default. I argued for turning on transient-mark-mode by default, and after decades that eventually happened.
The main reason delete-selection-mode is not on by default is inertia, aka tradition, I think. It is expected by most users of editors and other applications ...
[Posting this again here, but really think we ought to consider a policy of being able to close a question that duplicates one on StackOverflow.]
As it says here:
If you want to repeatedly yank the same text, use the secondary selection instead of the region or killed text.
What's missing from vanilla Emacs is a key binding to yank the secondary selection....
It's possible to use your keys much more efficiently when the mark is active than simply binding all of them to delete the region.
lispy is a nice example of this:
When the region is active, all keys a through z are bound to different commands.
When the region isn't active, all keys a through z self-insert.
Here's a simple example:
Finally I found a fix for the problem on emacswiki
(setq x-select-enable-primary t)
(setq select-enable-primary t)
(setq mouse-drag-copy-region t)
Quick tip: if you’re here looking to fix the fact that in Emacs shift-insert no longer pastes that text you highlighted with the mouse in your browser, the 2014 answer is to set x-select-enable-primary to true,...
Is this a bug?
No. To deactivate you have to use C-g or use one of the commands that operate on the region and deactivate as a side effect. This is described in the manual:
Whenever the mark is active, you can deactivate it by typing C-g (see Quitting). Most commands that operate on the region also automatically deactivate the mark, like C-x C-u ...