Your exactly right low voltage makes high amperage and things burn up and over heat. This is why the CUCV OEM starter relays fail. If you get a hint of low batteries charge them or replace them. Most times I just replace them. As many times as I start and stop a vehicle I have no issues with mine. If I need slave cables twice in a row. Load test the batteries and 9 out of 10 new batteries are needed. IMHO that is the problem. About 3-5 years and the batteries are toast. I use them hard plowing and jumping trucks and equipment.
Low voltage does not make high amperage. Low voltage makes low amperage (Voltage = Current x Resistance). What burns a starter at low voltage is the reduced cranking speed of said starter, via the amount of time a brush is in contact with each commutator piece on the armature while passing current. Proper brush motor is designed that each commutator segment simply wipes across the powered brush for a very small time, and the rest of it's rotation around is allowed to cool off before having its turn again on reheat. If we slow the starter down, while keeping it under the same load, we are greatly increasing the time spent on heating each armature commutator piece. Since they are simply copper, it does not take much heat to melt these segments completely. The faster a starter can spin, the longer the armature and brush life will be. On the solenoids, there is usually 2 coils within the solenoid, a "PULL" coil, and a "HOLD" coil. The pull coil is very powerful, enough to overcome cold, ice, water, dirt, and the internal return spring, all at the same time. It has to be strong enough to throw the starter pinion gear into the flywheel with authority level force nearly regardless of what is in its way. But this forceful coil generates too much heat to stay engaged, so, once engaged, it switches to a hold coil, which has enough power to hold the solenoid in the engaged position, but this coil alone does not have enough power to actually engage the solenoid. If the power to the starter is low, the solenoid may not fully engage, and remain on the pull coil circuit, which will quickly burn it up (this is where the starter will not shut off when key is released, because solenoid coil is so hot it is deformed internally, holding the solenoid plunger extended, and keeping the motor switch within it closed, continuing to crank the starter.). You don't have to actually pull and load test batteries, the vehicle itself is a great load test machine. Simply measure voltage during cranking. If below 10V on a 12V system, batteries are weak. Double for 24V. We all know the effect of low engine oil...