At least for Writer, Impress (Draw) this would make sense.
People that paste without thinking, just have text without formatting.
For other choices Paste special should be used.
Technically, when there is no text to paste, Past special should be presented, IMO.
For the position of the option, the following seem sensible:
In Writer "Tools > Options > Writer > Formatting aid"
In Impress "Tools > Options > Impress > General"
Yes please, paste into the current style at cursor location.
Guess it could eliminate a lot of Askbot questions like "how to eliminate links in text"
Just to make sure, that we are all on one page. This is really useful and I probably would enable it for myself. But this cannot be the default, amount of questions about "where did my italics/bold/underline go after pasting" would kill the askbot.
One of the features that I really miss when I have to work with Microsoft Office is Paste Special via short-cut. Libreoffice has this feature: Ctrl+Shift+V opens the dialog and you just have to press enter to get the clipboard content without formatting. Therefore an option makes not much sense (despite the fact that this function is a killer features for me).
Regardless of a default, it would be nice if the 'paste button' (and ctrl+v) acts according to the option chosen in its drop-down menu. In other words, to mimic the behavior already used to highlight text in writer: first choose a color with the 'highlight button', then it can be applied with only one click.