What is the reason to parenthesize <Plug> map names?

Thanks ZyX; your answer already covers the fundamentals, so let me just add why I've adopted the <Plug>(PluginNameAndMore) notation. (I think I saw it first in Kana Natsuno's plugins.)

Two reasons:

1. When wrapping a mapping with other stuff, it's easier to visually parse the individual mapping targets, like here:

   imap <C-x><C-c> <Plug>(CompleteStart)<Plug>(CamelCaseComplete)<SID>(CamelCaseCompleteModifyUndo)<Plug>(CamelCasePostComplete)<Plug>(CompleteoptLongestSelect)

2. When defining multiple mappings for a plugin, one must be careful that the LHS of one is not contained in another mapping. Otherwise, there will be a delay when the mapping is triggered, as Vim needs to wait for additional keystrokes before the ambiguity can be resolved. The closing parenthesis prevents any such ambiguity.

BAD                 GOOD
<Plug>MyFunc        <Plug>MyFuncNext, <Plug>(MyFunc)
<Plug>MyFuncReverse <Plug>MyFuncPrev, <Plug>(MyFuncReverse)

Parens make it clearer (to humans) when there are other keystrokes in a mapping following the <Plug> invocation. For instance I have this mapping:

nmap ]c <Plug>GitGutterNextHunkzv

That makes ]c jump to the next Git hunk and then do zv to open any folds there. But since <Plug> names are arbitrary, the command could have been called GitGutterNextHunkzv. In general there's no way for somebody reading a file using a <Plug> mapping to know if the whole thing is a name or there are other characters following.

If the GitGutter plug-in had used brackets for in the <Plug> name, it would be far clearer to see what's going on:

nmap ]c <Plug>(GitGutterNextHunk)zv

Both of {lhs} and {rhs} in the mappings command are byte sequences which can contain arbitrary data (except for NUL byte) as long as it has natural number of bytes (for {rhs} having zero number of bytes is also allowed). From this point of view (…) practice has no advantages over another one.

Specifically for (textobj-…) there is one minor advantage: you can select the whole {lhs} without <Plug> part with a) motion and have more readable dashes between words. I have no idea though why would one want to do so as the whole {lhs} can be selected with aW (with <Plug> part).

I do not see any reason for the LineJuggler version.

You should better ask authors about this. @IngoKarkat is here, on stackoverflow and will probably read the question soon. I have no idea how to contact Kana Natsuno.