You can just hit the option key to take a screenshot of an app without the shadow. No need to go and change system wide defaults
This is not necessarily supported everywhere though...
I also believe it should be the copy that strips the style.
FWIW, in my many decades of using computers, I've never once wanted to paste with styles as whatever app is getting pasted into inevitably (without exception, like 100% of the time) "guesses" the formatting incorrectly.
The default is crazy.