Yes, there is. "Best" is a harder subject to tackle, but there's always "better".

di{ is obviously both quicker and more precise than reaching to the mouse, pointing at the beginning of the code block, extending the selection until the end of the code block and hitting backspace.

One may think these keybindings are awkward or hard to remember (I did, at first, they are not) but they are both faster, more efficient and more deterministic by nature. But I may be a control freak. :-)

It's a subjective experience. I, too, prefer to use the keyboard as much as possible but I've also encountered doofuses that mock that position because the mouse is "so convenient" and "there's no way it's faster to use the keyboard entirely". So I guess their better is different from my better.

Good luck beaming your vim registers from a remote vim into the local clipboard.

That's why I prefer to use my local Vim (Emacs with evil-mode) and its remote editing features (Tramp).