Raspi, the feature you request may, in a way, already exist. It is the keyboard shortcut Ctrl + . (That last charcter is a period)

Documentation

I will offer a view from someone in the development arena but not a part of the User Interface team. This is neither as simple as matching to outer brackets (that successive clicking mentioned) nor Un/Comment. The reason is it will need to account for all elements in an expression rather than just the one highlighted. That is, if you highlight the third element and click twice you get the full expression. You are asking for parenthesizing all elements in this expression, not just the third. So there is more matching to be done. And this will need to be sensitive to the formatting. It can be done for StandardForm and InputForm. For FullForm there is no need. Can it be done for TraditionalForm? I don't know.

Again from the point of view of a developer, I would ask these questions. (1) What problem(s) does this solve? (2) How important is this feature? (3) Can these problems be tackled in different ways? (Obviously item (3) has bearing on item (2)). In this case, the problem solved is one of giving a relatively simple interface for parenthesizing infix and postfix operators. Which has use for say visual purposes (hence possibly is applicable in education environments). That stated, others have shown ways to do this, at least for simple cases, using programmatic means. Were I in the user interface group, and knowing what little I do of the functionality they tackle and the issues they need to address, I myself would not give this above low priority. To be fair, it's not functionality I myself would use, and of course that will have a negative influence on my opinion. But I remain stuck on item (2): is this really so important? Me, I want to have better formatting of mathematics (think: LaTeX layout). I want reliable exporting to PDF. I want better exporting to LaTeX. I'd like an ability to enter bibtex as associations and have it format to bbl. I have a number of other items on my wish list that are less geared to "academic paper" type needs but nonetheless involve the user interface.

I'm not claiming this suggestion lacks merit. I simply do not see it as something in which to sink more than a small amount of time. If it requires more (something I lack the expertise even to guess at) then I'd favor not pursuing it. Again, just my opinion.

Hi Raspi,

not really what you want, but here is at least a simple function for examining expressions:

Attributes[makeObvious] = HoldAll;
(* makeObvious[expr_]:=Framed//@HoldForm[expr] *)
makeObvious[expr_] := Map[Framed, HoldForm[expr], {2, Depth[expr] - 1}]

With this we get e.g.:

A basic implementation to parenthesize a selection would be as follows:

b1 = Button["Parenthesize selection", Module[{x},
  x = CurrentValue["SelectionData"];
  NotebookWrite[ButtonNotebook[], RowBox[{"(", x, ")"}]]]]

And this is the inverse (assumes the selection includes the parentheses):

b2 = Button["Unparenthesize selection", Module[{x},
  x = CurrentValue["SelectionData"];
  NotebookWrite[ButtonNotebook[], Part[x, 1, 2]]]]

You can add these buttons to a docked cell to make available for all notebooks:

SetOptions[$FrontEndSession, 
 DockedCells -> {Cell[BoxData[ToBoxes@Row[{b1, b2}]]]}]

Change \ $FrontEndSession to \$FrontEnd to have it persist between restarts of the frontend.

Change things back with:

SetOptions[$FrontEndSession, DockedCells -> {}]

DISCLAIMER: This is just a simple prototype I wrote for you to experiment with. Implementing something like this that is production-grade is quite complicated because it needs to support large amount of edge cases (which this does not do). I won't be able to make improvements upon this, but you are welcome to (and anyone reading this is welcome to). This is not functionality I would use myself, because I prefer to write Wolfram Language code that is human readable in the first place (by limiting the amount of syntactic shortcuts).

Thanks Peter for your reply! I conclude that the status of my suggestion/request/idea is then "suspended" for the time being, which is a neutral word for saying that a decision/discussion hasn't been made about the suggestion or has been put on hold (for unknown reasons, maybe lack of manhours/time/urgency/priority) and, once it gets seriously discussed among them with the aim to finally take a decision (to adopt vs. to reject), there could still be a chance of rejection, in the end.

Lemme wait another year (time flies!), but next year I'd surely love to hear a clear status change. Chatting with the developers (phone, lunch, fair, camp, assembly, conference, party, pub, etc), one should be able to get some word/half-baked information out, e.g. if they are fond of the suggestion in principle, and if they could ballpark what the odds are that the feature gets implemented at all.

@Peter Maybe you get a chance to produce the desired bit of information after all … , thanks in advance for your help re this matter. As you could imagine, I would be elated to hear something like "raspi, in favor of just you, I did manage to get a word … and they believe the odds are only 20% that your nice idea gets implemented within the next 5 years, meaning that it's definitely not off the table, it actually made it on the to-do-list schedule (congrats raspi!), flagged with the lowest priority imaginable. So it'll come, but you shouldn't hold your breath since nobody knows what the world, or the team/company for that matter, will look like in 5 years."

Thanks for thanking, the prospect (let me have some hopes up for this proposed new feature - your team might decide against it eventually, haha) and your attention @Peter, @Arnoud, @Karl, appreciated ymmd!

Crossing fingers, I would really enjoy and profit from such a feature in the GUI of Mathematica! And not only me, I am sure ::))

I will use your linked Product Feedback Form in future, too. Good to know, thank you.

Hi Hans, thanks for participating in the discussion. I am fully aware of that functionality: we can leap around with the mouse pointer and then click around (or use your keyboard shortcut) to get an idea of 'the next bigger balanced compound expression'. Even in your example there's quite some clicking (and memorization) involved and once the selection is gone, the information/clarity about the grouping is lost.

My ultrashort algebraic example wasn't a good example anyway. Better examples involve a combination of pure functions, patterns, Boolean operators, conditionals, summation/integration symbols, rules, and alike; there we learn that we must place parentheses! Usually for conciseness and elegance we do not write down superfluous parentheses or we simply forget to write them, when they're needed. Seeing parentheses, even if they are indeed superfluous, can help intelligibility and provides unambiguousness to the reader.

So, your "Ctrl + ." comes first, yes, and for some users/uses it might be enough. It selects a balanced expression and the selection expands to compound expressions depending on the position of the mouse pointer (poor mouse pointer placement shown hehe):

Then my "Show Groupings" comes next, it makes all (or all relevant) groupings within that pre-selected compound expression readily visible to any reader, not just to the person with the keyboard/mouse ;-)

Mind you, on a print-out (paper, book, screenshot) one cannot click around anymore. In such a case, unambiguous code like a+((b/c)*(d^e)) proves to be a good alternative to the reader/debugging user. In summary, "your" and "my" features go well together/belong together/complement each other, yes, but in terms of practical usage they are different enough.