"I would like to have a cat, provided it barked" states that U(barking cat) > U(no cat) > U(nonbarking* cat). Preferring a meowing cat to no cat is a contradiction of what was stated. The issue you raise can still be seen with U(barking cat) > U(barking dog) > U(no pet) > U(nonbarking cat), however - a belief in the attainability of the barking cat may cause someone to delay the purchase of a barking dog that would make them happier.

*In common usage, I expect that we should restrict it from "any nonbarking cat" to "ordinary cat", based on totally subjective intuitions. I would not be surprised by someone who said "I would like an X, provided it Y" for a seemingly unattainable Y, and would not have considered whether they would want an X that Z for some other seemingly unattainable Z. I think they just would have compared the unusual specimen to the typical specimen and concluded they want the former and don't want the latter. This is mostly immaterial here, I think.