As far as I can tell, the main thing they offer is an additional point of failure. Some parks go for seatbelts on restraints because their insurer believes that the restraint on its own does not have enough points of failure to make the risk low enough for their liking. Restraints have multiple points of failure built into them anyway, but a seatbelt adds an extra point of failure on top of that.
The only way a seatbelt would categorically save someone is if all the points of failure built into the restraint itself fail at once, and the chances of that are practically zero due to how many points of failure are built into modern coaster restraints.
There may also be an element of "safety theatre" in seatbelts, though. Even though they aren't expressly needed, having an additional seatbelt may make some guests feel safer.
Seatbelts on their own do little to none of the heavy lifting in terms of actually keeping a rider's restraint down, though; as those "OMG MY BELT CAME LOOSE!" viral videos on YouTube show, the seatbelt being undone during the ride does not make the rider any less secure within the restraint in real terms.
EDIT - As an example, I think this video shows how the seatbelt ultimately does very little of the heavy lifting in terms of keeping the rider secure within the restraint: