For the sample data, your y-values are monotonic. If this is generally true, there's no point in including them in the comparison.

my $modified = reduce{
    my( $x1, $y1, $x2, $y2 ) = ( @{ @{ $a }[ -1 ] }, @$b );
     $x2 < $x1 ? pop @{ $a } : push @{ $a }, $b;
    $a;
} [ shift @points ], @points;
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Assuming you necessarily hold all data in memory, you could also use splice in a while, which feels more natural to me:

my $i = 1;
while ($i < @points) {
    if ($points[$i-1][0] > $points[$i][0]) {
        splice @points,$i-1,2;
        --$i or $i = 0;
    } else {
        $i++;
    }
}
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or just a streaming push/pop, which is algorithmically what you've done, but reads better, I think.

my $modified = [];
for my $point (@points) {
    if (@$modified and $modified->[-1][0] > $point->[0]) {
        pop @$modified;
    } else {
        push @$modified, $point;
    }
}
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I'd like there to be a more streaming solution here, but there's no way to tell if the first point should have been accepted until you are past halfway in the list, and you don't a priori know how long the list is.

Golfed:

my @m;
@m&&$m[-1][0]>$_->[0]?pop @m:push @m,$_ for @points;
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