Your first output doesn't match your first program, since the variable $test is not printed in the BEGIN block. I suppose this is because you couldn't compile with strict, the solution to that is to declare the variable with our (which will just alias $test to $main::test). Having lexicals override package variables, and our variables (locally aliased? I can't remember if there's a standard name for those) is true even without the -s switch. Actually the $test in the BEGIN block and the $test after the my declaration are two different variables that happen to have the same name. Without strict, the fact that a -s variable is a package global can be implicit.
On the main subject now, on whether -s should be used/kept: I like that perl allows unsafe but useful features that you can use for oneliners and other throwaway code. So having an option with some caveats is OK for me, I just try to avoid them when I'm not writing in a console. The thing is, having a "rudimentary switch" mechanism for any kind of program means that you intend to use it several times, or even that you may not be the only one to use it. For me this is not compatible with the shortcomings of -s, so I would never use it. But I like how perl's philosophy is to "give the user enough rope to hang themselves" but tell them how to avoid the pitfalls, rather than try to secure everything and remove the need for a better understanding. So remove -s, why not? But since it is little known option, and it does have its advantages when used correctly, I don't think it's that much of a hazard (unlike <> or the two parameters open, which are not only really common, but also more standard).