That's because defining named subroutines is done at compile time. Here's an illustrative example:

sub a {
   sub x { print "I came from a\n"; }
}

sub b {
   sub x { print "I came from b\n"; }
}

x();
a(); x();
b(); x();
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This generates:

I came from b
I came from b
I came from b
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To do things your way you can localize the subroutine name, i.e.:

sub a {
    local(*x) = sub { "from a" };
    doit();
}

sub b {
    local(*x) = sub { "from b" };
    doit();
}

sub doit {
    print "I came ", x(), "\n";
}
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