You've put your chaining at a disadvantage in the ugliness department by illustrating it with mutators of $_. This technique shines in combination with other list operators like grep and sort, and when wrapped in a subroutine so that it acts on a copy of @_.

sub quux {
    my @args = @_;
    map { foo $_ }
      map { bar $_ }
        map { baz $_ } @args;
}
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The real alternative is nested sub calls. While those look messy in C, with all the parens to be balanced, they have an equally nice expression in Perl, my $quux = foo bar baz $_;

One of the better reasons to use map in this way is the aliasing of localized $_ to each argument in turn. That is not a big advantage in your actions on a list of one element, but is a nice shorthand when operations act on $_ by default. You missed an opportunity to use that in the map { uc } stage.

Of course, this is all extremely powerful when acting on lists. The Schwartzian Transform is on anybody's list of "Best Dressed Perl".