It's got nothing to do with BEGIN being sub-like. Inner subs would have to capture every time the outer sub is called. But since there are no private subs in Perl, there isn't necessarily any executing outer sub to capture from.

sub outer {
   sub inner {
   }
}
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is basically

sub outer {
   BEGIN {
      *inner = sub {
      };
   }
}
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Replace it with

sub outer {
   *inner = sub {
   };
}
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and inner will capture properly for an inner sub. Of course, problems will still ensue if you call inner() from outside of outer(). To solve that, you'd need a language feature such as

sub outer {
   my sub inner {
   }
}
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