If you use use strict;, you have to declare all variables with 'my',

That's a bit of an over-simplification. See the discussion of use strict 'vars' in perldoc strict.

This generates a compile-time error if you access a variable that wasn't declared via our or use vars, localized via my(), or wasn't fully qualified.

Using my is only one of a number of ways to satisfy use strict 'vars' - albeit the most common.