But if that case is not-so-common, then you don't need my at all.
my forces you to predeclare variables. This is highly important, as Perl can then tell you if you misspell a variable.
It has the additional advantage of allowing you to explicitly declare the scope of a variable, to tell Perl whether you meant to create a new, lexically scoped variable or whether you meant to use the global variable.
I think most of your complaints can be done away with by not using strict. Then you don't need to predeclare your variables but still can use lexical variables with my. Of course, recursion is a harsh mistress if you're using global variables. Typos also are a nasty problem. But you don't seem to have these.