Can we use CUPED if correlation between control and treatment equals to 1?

Question

We know that Var(Y_cuped) = Var(Y)(1-p²), where p is a correlation between control and treatment, and I have a metric with Corr(X, Y) = 1. It means that CUPED, in such cases, can reduce variance to zero, Var(Y_cuped) = 0.

More about CUPED: https://matteocourthoud.github.io/post/cuped/

Does it mean that something wrong with my metric, or should I use other variance reduction techniques? When can we use CUPED for variance reduction? Does CUPED have some usage constraints?

P.S.: My metric is zero-inflated; I have 98% of zeros in control and treatment groups