Then you couldn't have multiple variables with the same name, as in:

my $x;

sub foo {
   my $x;
   my $x;
   {
      my $x;
   }
}

sub bar {
   my $x;
}
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It seems to me that your code behaves almost exactly like

our $x;

sub foo {
    local $x;
    local $x;
    {
        local $x;
    }
}

sub bar {
    local $x;
}
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^* Of course, since neither code does anything, this might be an even more vacuous statement than is usual for me. :-)
^** Ah, but the $x of local $x is the same variable as that of our $x, whereas the $x of my $x is not the same variable as that of the other my $x.

local doesn't create variables. It just backs up the value of the variable and restores it later. While it reduces the problems of using global variables, it doesn't remove them all.

local doesn't create variables. It just backs up the value of the variable and restores it later.

I know ^*. Certainly there's an internal difference; but it seems to me that the casual user is not likely to encounter much difference between

our $x;
CODE INVOLVING OUTER $x
{
    local $x;
    CODE INVOLVING INNER $x
}
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and

my $x;
CODE INVOLVING OUTER $x
{
    my $x;
    CODE INVOLVING INNER $x
}
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That's by no means to say that there is no difference—indeed,

our $x; my $y;
sub twiddle { $x = $y = 'twiddled' }
{
    local $x = 'local?';
    my $y = 'local!';
    twiddle;
    say $x, ', ', $y;
}
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shows that there is—just that one's not likely to see it in casual use.

^* Ah, but re-reading shows that I didn't seem to understand: I said something about having two variables with the same name, when really the localised $x is the same variable as the original one, just with a ‘temporary’ value. Is that misstatement on my part what you were correcting?