I'm going to guess you are using a phone rather than a computer or tablet. If you can make the photos twice the size, that will help.
Lets start with this question. The protection is based on the weakest item in the system or the weakest wire that we don't want to have burn if there is a short or overload.
It doesn't matter what the alternator can produce.
Nor does it matter how big the battery is. Even the smallest battery capable of starting your car's engine is capable of supplying a couple of hundred amps!
However, if the car has a 60 amp factory alternator, then the car was originally equiped with a bigger battery and a heavy duty wiring. I think your photos show some of that.