And that's exactly what I want to enforce.

You get that behaviour out of the box:

{
    package FOO;
    use Data::Dumper;
    print Dumper \"bar";
}
print Dumper \"baz";
__END__
Name "main::Dumper" used only once: possible typo at - line 7.
$VAR1 = \'bar';
print() on unopened filehandle Dumper at - line 7.
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However, if you call Dumper by its fully qualified name (ie Data::Dumper::Dumper, or IO::Socket::INET->new in your example), there's no way to prevent it from working:

{
    package FOO;
    use Data::Dumper;
    print Dumper \"bar";
}
no Data::Dumper;   ## not even this
print Data::Dumper::Dumper \"baz";
__END__
$VAR1 = \'bar';
$VAR1 = \'baz';
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