Poor electrical connections
The extra resistance of poor connections in a circuit will not cause higher current flow thus burning up something but will actually reduce the overall amps used in the circuit. This is because it is increasing the circuit's resistance along a single path. What can happen is you can get local heat build up at the poor connection causing the circuit to burn open or a short due to heat breakdown of insulation.
The more power the circuit carries the more likely it is to burn up due to a poor connection. This type of thing was common with aluminum house wiring causing fires. The wire from the positive battery terminal to the starter relay is aluminum and carry high amps. They normally fail because of resistance buildup due to corrosion not over heating in the process.
Over all resistance can build up in the starter control circuit through the starter switch to the starter relay to the point that starter relay doesn't get enough current to operate. You normally don't burn up the starter switch or any connectors there because most people have enough sense not to leave it powered until something melts. The first thing to do is check the starter relay bypassing the normal switch and wiring with a remote switch. (Some newer cars have problems with this.) Then bypass the normal starter switch but not the normal wires. Continue with this until the problem is found.
I once had a problem with a loose terminal on the fuse block found by wiggling the wire. Nothing was overheated. Engines with computer controls often with fuel injection are super sensitive to poor connections with the most common problem area dirty corroded ground connections. When you see a car with one bright head light and one dim head light, the dim light will probably have a bad ground connection to the frame, without burned up wiring due to the poor ground.
While auto electrical circuits could burn out due to a poor connection they normally don't. They do get fried or the fuse opens because excess current caused by shorts. Shorts are most often thought as, to ground, but they can be internal in devises such as relay coils, ignition coils and others that have a internal brake down of resistance causing excess current flow. Yes it could be because of excess heat breaking down insulation due to a poor connection who can tell.
Things fail due to use, age, abuse and poor design.