Question about @Sendable checking

We've been trying out -Xfrontend -warn-concurrency, and I'm getting a warning that I don't understand.

class SendabilityTester {
    var name: String = ""

    func test() {
        print("name outside: \(name)")
        Task {
            // Capture of 'self' with non-sendable type 'SendabilityTester' in a `@Sendable` closure
            print("name inside: \(name)")

SendabilityTester itself is not Sendable, nor is it isolated to @MainActor. However, as I understand it, the nested Task here is going to inherit @MainActor isolation from the surrounding function. We don't get a warning when accessing outside the Task, and it seems like it should be equally safe to access name from within another @MainActor-isolated task.

The warning the compiler emits is accurate in a sense—we are capturing self within a @Sendable closure, and self is not marked as Sendable. But should this warning be disabled when declared within an actor-isolated function, if the closure itself is known to also run on that same actor?