Is AsyncTask really conceptually flawed or am I just missing something?

How about something like this:

class MyActivity extends Activity {
    Worker mWorker;

    static class Worker extends AsyncTask<URL, Integer, Long> {
        MyActivity mActivity;

        Worker(MyActivity activity) {
            mActivity = activity;
        }

        @Override
        protected Long doInBackground(URL... urls) {
            int count = urls.length;
            long totalSize = 0;
            for (int i = 0; i < count; i++) {
                totalSize += Downloader.downloadFile(urls[i]);
                publishProgress((int) ((i / (float) count) * 100));
            }
            return totalSize;
        }

        @Override
        protected void onProgressUpdate(Integer... progress) {
            if (mActivity != null) {
                mActivity.setProgressPercent(progress[0]);
            }
        }

        @Override
        protected void onPostExecute(Long result) {
            if (mActivity != null) {
                mActivity.showDialog("Downloaded " + result + " bytes");
            }
        }
    }

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);

        mWorker = (Worker)getLastNonConfigurationInstance();
        if (mWorker != null) {
            mWorker.mActivity = this;
        }

        ...
    }

    @Override
    public Object onRetainNonConfigurationInstance() {
        return mWorker;
    }

    @Override
    protected void onDestroy() {
        super.onDestroy();
        if (mWorker != null) {
            mWorker.mActivity = null;
        }
    }

    void startWork() {
        mWorker = new Worker(this);
        mWorker.execute(...);
    }
}