It can protect you when your tests end unexpectedly. For example, let's say you're running 30 tests. At some point, another programmer on your team writes a bad function which calls exit. Your tests might end prematurely and having a test plan catches that. Or maybe you've just updated a CPAN module which calls exit when it shouldn't or finds some other way of terminating your tests early. Again, having a test count will protect you. It's quite possible that a test can terminate early without any tests failing.

Another example is when someone does something like this (assumes Scalar::Util::looks_like_number() has been imported):

foreach my $num ( $point->coordinates ) {
    ok looks_like_number($num), "... and $num should be a number";
}
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If that returns a different number of coordinates from what you expect, having a test plan will catch that. Admittedly, this should actually look something like this:

ok my @coordinates = $point->coordinates, 
  'coordinates() should return the coordinates';
is scalar @coordinates, 3, '... and it should return the correct numbe
+r of them';
foreach my $num ( @coordinates ) {
    ok looks_like_number($num), "... and each should be a number ($num
+)";
}
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With that, because you're explicitly counting the number of coordinates, the test plan is not as necessary. However, as with the exit example, a test plan not only helps out when the code is less than perfect, it also helps out when the tests are less than perfect. It's such a small thing to update and when it actually catches a problem, you'll be greatful.

Some people argue, "yeah, but I never write code that stupid so this doesn't apply to me!". That's fine. If updating the test plan is too much work for them, so be it. Me, I know I make mistakes and I expect others to make mistakes. If we didn't make mistakes, we wouldn't need the tests in the first place.

(Trivia quiz: if the above tests were in a CPAN module, how might those tests fail?)