How can I reliably simulate touch events on Android without root (like Automate and Tasker)?

As suggested, the best way to simulate touch events since Nougat (API 24) is by using an accessibility service and the AccessibilityService#dispatchGesture method.

Here is how I did to simulate a single tap event.

// (x, y) in screen coordinates
private static GestureDescription createClick(float x, float y) {
    // for a single tap a duration of 1 ms is enough
    final int DURATION = 1;

    Path clickPath = new Path();
    clickPath.moveTo(x, y);
    GestureDescription.StrokeDescription clickStroke =
            new GestureDescription.StrokeDescription(clickPath, 0, DURATION);
    GestureDescription.Builder clickBuilder = new GestureDescription.Builder();
    clickBuilder.addStroke(clickStroke);
    return clickBuilder.build();
}

// callback invoked either when the gesture has been completed or cancelled
callback = new AccessibilityService.GestureResultCallback() {
    @Override
    public void onCompleted(GestureDescription gestureDescription) {
        super.onCompleted(gestureDescription);
        Log.d(TAG, "gesture completed");
    }

    @Override
    public void onCancelled(GestureDescription gestureDescription) {
        super.onCancelled(gestureDescription);
        Log.d(TAG, "gesture cancelled");
    }
};

// accessibilityService: contains a reference to an accessibility service
// callback: can be null if you don't care about gesture termination
boolean result = accessibilityService.dispatchGesture(createClick(x, y), callback, null);
Log.d(TAG, "Gesture dispatched? " + result);

To perform other gestures, you might find useful the code used for testing the AccessibilityService#dispatchGesture implementation.

EDIT: I link a post in my blog with an introduction to Android accessibility services.