>> I'd expect TAB rather to iterate over multiple matches,
>> i.e. like TAB in browsers go to the next match.  Even in the *Completions*
>> buffer TAB moves to the next completion.  And in icomplete-mode
>> the closest analogy to picking one result is 'C-j'
>> (icomplete-force-complete-and-exit).
>
> If people like it, I'm totally fine with changing the binding to 'C-j'.

I'm very sorry for beating this horse again, but after trying to use xref
as a replacement of grep, typing 'C-x p g' pops up a grep-like buffer
and due to habit of typing the same keys that are supported by grep-mode
where among them is TAB bound to compilation-next-error to browse the
results forward, but instead of going to the next match, it does the
worst thing imaginable - kills the output buffer.

Therefore, I propose this patch that binds TAB and S-TAB to command
that behave like compilation-next-error and compilation-previous-error: