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The OP's use case was too simplified to convey
the usefulness of fileinput.islastline().  It does not
just save a couple of lines.  I am attaching a "wc" or
"word count" program to demonstrate.  Note the following
problems with the current work-around:

1. Instead of doing end-of-file processing at the end of
   a file, we must do it at the beginning of the *next*
   file.

2. Useful functions such as fileinput.filelineno() and
   fileinput.filename() now refer to the *wrong* file,
   so now we need to manually keep track of these values
   ourselves.

3. Perhaps a minor point, but this work-around only works
   at the *beginning* of the loop instead of the end.  It
   feels somewhat awkward.

4. End-of-file processing must occur both in the loop and
   once outside.  A function avoids code duplication, but
   to refer to variables in the loop, they must be passed
   into and out of the function (6 in, 2 out for the "wc"
   example... maybe keyword arguments would have helped).

5. Most important is readablility.  It's not obvious that
   `fileinput.isfirstline() and fileinput.lineno() != 1`
   means we are the end of the (previous!) file.  Using
   `fileinput.islastline()` would be much clearer.

And not that it is a reason, but Perl and Ruby solve
this with an `eof` function and `eof?` method,
respectively.