There is a website in Brazil that allows users to set price alerts regardless of dates (voopter.com.br). All you have to do is set a departure and destination airport and select the highest fare you would be willing to pay (be it a one-way or round trip). It's a collaborative platform, so the more people search flights on it, the higher are the chances to be alerted. Unfortunately, it's not a widespread website, but I still manage to receive alerts for popular destinations all the time. I love it because they use several other flight search platforms so you don't have to spend time looking around.
That's how I think Google should do, too. People are constantly searching for flights on Google Flights, so they could use these cheap flight results originating from other people to alert flexible travelers. It's quite easy to determine whether a flight is cheap or not based on its price history. Actually, your alerts would be based on the highest acceptable price you select on the platform.