This would introduce inconsistency with the fact that async and throws are keywords for denoting effects and already have their own set of "rules". Both are parts of their type signatures, (Int) -> String and (Int) async -> String are different (even though they have a certain subtyping relationships), while (Int) mutates -> String does not make sense as a standalone type signature. Effectful read-only properties were introduced in SE-0310, allowing get async and get throws in property declarations. In the light of that, what would get mutates even mean?
Additionally, throws has counterparts in throw and rethrows. async has await and potentially reasync, as discussed in future directions of the corresponding proposal. I don't think mutate and remutates make sense even at a conceptual level. In this sense, taking, borrowing, and mutating are not function/property effect modifiers.