Are the effects of /s really wanted here?

Yes, because without /s the newlines are not matched.

#!/usr/bin/env perl 
use strict;
use warnings;
use Test::More tests => 2;

my $q = 'qqqweqwe
asdasdasd
zxczxczxc
tyutyutyi
';
my $a = 'zxczxczxc';
my $want = "\ntyutyutyi\n";

my $t = $q;
$t =~ s/^.*$a//sm;
is ($t, $want, "With /s - matched");

$t = $q;
$t =~ s/^.*$a//m;
isnt ($t, $want, "No /s - not matched");
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