How to make AVSpeechSynthesizer work for write and delegate (Big Sur)

You are 100% correct.

The utterance aloud completed but nothing else worked.

I mistakenly thought the process would remain in memory until the completion of speech and the associated delegates fired.

For those who may need a working solution, here it is.

class SpeakerTest: NSObject, AVSpeechSynthesizerDelegate {
    let synth = AVSpeechSynthesizer()

    override init() {
        super.init()
        synth.delegate = self
    }

    func isSandboxEnvironment() -> Bool
    {
        let environ = ProcessInfo.processInfo.environment
        return ( environ["APP_SANDBOX_CONTAINER_ID"] != nil )
    }

    func speechSynthesizer(_ synthesizer: AVSpeechSynthesizer, didFinish utterance: AVSpeechUtterance) {
        print("Utterance didFinish")
    }

    func speechSynthesizer(_ synthesizer: AVSpeechSynthesizer,
                           willSpeakRangeOfSpeechString characterRange: NSRange,
                           utterance: AVSpeechUtterance)
    {
        print("speaking range: \(characterRange)")
    }

    func selectVoice(targetSpeaker: String, defLangCode: String) -> AVSpeechSynthesisVoice
    {
        var usedVoice   = AVSpeechSynthesisVoice(language: defLangCode) // should be the default voice
        let userCode    = AVSpeechSynthesisVoice.currentLanguageCode()
        let voices      = AVSpeechSynthesisVoice.speechVoices()
        for voice in voices {
            //        print("\(voice.identifier) \(voice.name) \(voice.quality) \(voice.language)")
            if (voice.name.lowercased() == targetSpeaker.lowercased())
            {
                usedVoice = AVSpeechSynthesisVoice(identifier: voice.identifier)
                break
            }
        }
        // ensure we return a valid voice
        if (usedVoice == nil) {usedVoice = AVSpeechSynthesisVoice(language: userCode) }
        return usedVoice!
    }

    func speak(_ string: String, speaker: String) {
        let utterance = AVSpeechUtterance(string: string)
        utterance.voice = selectVoice(targetSpeaker: speaker, defLangCode: "en-US")
        synth.speak(utterance)
    }

    func writeToBuffer(_ stringToSpeak: String, speaker: String)
    {
        print("entering writeToBuffer")
        let utterance   = AVSpeechUtterance(string: stringToSpeak)
        utterance.voice = selectVoice(targetSpeaker: speaker, defLangCode: "en-US")

        synth.write(utterance) { (buffer: AVAudioBuffer) in
            print("executing synth.write")
            guard let pcmBuffer = buffer as? AVAudioPCMBuffer else {
                fatalError("unknown buffer type: \(buffer)")
            }
            if ( pcmBuffer.frameLength == 0 ) {
                print("buffer is empty")
            } else {
                print("buffer has content \(buffer)")
            }
        }
    }

    func writeToFile(_ stringToSpeak: String, speaker: String)
    {
        let utterance = AVSpeechUtterance(string: stringToSpeak)
        var output    : AVAudioFile?
        let desktop   = "~/Desktop"
        let fileName  = "Utterance_Test.caf" // not in sandbox
        var tempPath  = desktop + "/" + fileName
        tempPath      = (tempPath as NSString).expandingTildeInPath
        // if sandboxed, it goes in the container
        if ( isSandboxEnvironment() ) { tempPath = "Utterance_Test.caf" }

        utterance.voice = selectVoice(targetSpeaker: speaker, defLangCode: "en-US")

        synth.write(utterance) { (buffer: AVAudioBuffer) in
            guard let pcmBuffer = buffer as? AVAudioPCMBuffer else {
                fatalError("unknown buffer type: \(buffer)")
            }
            if ( pcmBuffer.frameLength == 0 ) {
                // done
            } else {
                // append buffer to file
                if ( output == nil ) {
                    let bufferSettings = utterance.voice?.audioFileSettings
                    output = try! AVAudioFile( forWriting: URL(fileURLWithPath: tempPath),settings: bufferSettings!)
                }
                try! output?.write(from: pcmBuffer)
            }
        }
    }
}

class ViewController: NSViewController {
    let speechDelivery = SpeakerTest()

    override func viewDidLoad() {
        super.viewDidLoad()

        let targetSpeaker   = "Allison"
        var sentenceToSpeak = "This writes to buffer and disk."
        sentenceToSpeak    += "Also, 'didFinish' and 'willSpeakRangeOfSpeechString' delegates fire."

        speechDelivery.writeToBuffer(sentenceToSpeak, speaker: targetSpeaker)
        speechDelivery.speak(sentenceToSpeak, speaker: targetSpeaker)
        speechDelivery.writeToFile(sentenceToSpeak, speaker: targetSpeaker)
    }

    override var representedObject: Any? {
        didSet {
            // Update the view, if already loaded.
        }
    }
}

Why export wav format that can't play, but caf format is OK?