The solenoid draws far more current than a relay because it is pulling the bendix as well as closing the contacts, don't have the numbers in front of me. Using a relay in the starter solenoid ckt has become almost universal in the automotive world in the last 10 yrs, several mfgs have even had recalls to retrofit a relay. Chevy cavalier and Hyundai come to mind. I am adding one to the starter ckt on the Push, hotrodders commonly use them.
Most often the reason for the recall is that on cars that dont have the firewall/fender mounted solenoid, the cable from the battery to the starter is ALWAYS live. Abrasion, touching a hot exhaust etc can cause it to ground and start a fire., installing the upper solenoid makes it so the cable is only live while the starter is actually in operation.
The old Fords all had fender mounted solenoids, If the wire abraded, the only issue noticed was that the starter stopped working. With a chevy (starter mounted solenoid) if you were LUCKY, the car would die, and the battery would discharge, if you weren't so lucky the jacket would start to smoulder and burn.
That's also why offroaders and racers make the mod, it's for safety
With newer cars and their tighter engine compartments, the cable often has to run all the way around the engine passing very close to the exhaust and potential abrasion points, so a long live wire is a fire just waiting to happen.
Ken.