The phrase "the fuse protects the wire" is true-ish, but kind of misses the point.
A wire of a given size can carry so much power before it heats up, melts its insulation, and starts a fire. The exact math of that is tricky because insulation type, environment temperature, airflow, wire material/form, and a variety of other factors play into the final numbers.
In the case of cars, you can get a table online that shows the safe current for a given wire size. If your fuse is larger than the safe value, then the wire itself will become the fuse and you risk electrical fires.
You can *also* spec your fuse size to protect whatever is on the circuit, as long as you stay below that safe value.
As a rule of thumb, the fuse should be as close to the battery/alternator as feasible because if you get a short between the fuse and the battery you won't have any protection.
Here is a
good reference for automotive wire sizes.
