If it's anything like the UK then it's likely the games are played in a public space like a park, so it might not be possible to eject the parent.
* All of the parents already know who the abusive parent is
* The first warning was the coach talking to the "entire group" (at a natural stopping point). The group dialed it back (there will always be some controversial calls), but that one parent didn't get the message.
* Finally, the game stopped suddenly (ball was in play, but in a neutral position) and they we're directly addressed by the ref.
This caught the abusers attention. This was an abnormal event. They were being addressed directly. Whether they realized they were the problem, they certainly recognized the social pressure. They recognized how embarrassing it was (sadly, they probably didn't realize how embarrassing it was for their kid) and decided to take the ref's suggestion to cool down.
Keep in mind these refs are often volunteers, working solo, have no official connection to the teams or field owners.
And there is a ref shortage virtually everywhere, at all levels and sports. Making it more difficult just isn't realistic.
You don't want to be the reason your kids team lost. You don't want your kid getting kicked of their team for your behavior.