>> How so?  AFAICS, it's the exact same kind of output, except that it 
>> gets truncated.  And it's (obviously?) better to see the context of the 
>> pattern you are searching for, instead of the first characters of the 
>> lines on which the pattern is found, in which the pattern might not be 
>> present.
>
> Since Grep doesn't return the column number of the match, we get it from 
> parsing the string again. And if the string is now modified to be 
> truncated from both sides, the column number will become wrong.
>

I did not understand that you need the column number of the match.  That 
could perhaps become a feature request for GNU grep: with -o and -n, also 
print the column number of the first character.

That being said, if you truncate the N first characters of the matching 
line, you have to parse the original line (that is, not the line that grep 
or another tool outputs) to find the matches anyway.