BTW This difference does not fit into the philosophy of Perl, where you should not be able to distinguish between strings and numbers, so this is actually a language design flaw.

Agreed. Perl always had the philosophy that the operators determine the operation, not the type of the operands. Perl 6 solves this by adding type modifiers for the bitwise operators:

  $a +| $b;  # Integer bitwise OR
  $a ~| $b;  # String bitwise OR
  $a ?| $b   # logical OR
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It makes the bitwise operators look a bit more ugly, but I don't really mind because I don't use them very often. This change has the additional benefit of freeing up the characters that perl 5 uses for bitwise operators.

(Note that || as a logical OR still exists; the difference is that || returns the first true value, whereas ?| always returns a Bool).