>>    This said, IMNSHO the feature we're talking about shouldn't be implement
 >>    in lisp-mode and c-mode but directly generically in
 >>    indent-for-tab-command.
 >>
 >>If that works, by all means do it.

FWIW all indent-line-functions with the exception of `lisp-indent-line'
either don't have arguments or, like `c-indent-line', `f90-indent-line',
and `(c)perl-indent-line' expect completely different arguments here.
Hence a generic solution seems hardly practicable.

For the case a prefix argument is given and the region is not active, we
could try to set the region around the smallest containing form and call
`indent-region' on that.  But that would be a different feature.

 > I'd certainly be grateful!
 >
 > [I didn't realize I used it so much (on the face of it, it seems like a
 > rather obscure bit of functionality), but I find my fingers keep trying
 > to invoke it, and I keep being surprised when it doesn't work...  ]

For `lisp-indent-line' I can offer the attached patch.