Engine ground strap

If one was to forget to install the engine to engine mount ground strap and tried to start the engine, of course the shielding will melt off on the wires the ground chooses to pass. I’m wandering if the control cables could also be effected with no signs of deterioration only to fail later. Can they be inspected for issues somehow?
Thanks

I made a pre purchase inspection on a plane some years ago.
This revealed that no engine ground strap was installed.
The seller had operated the plane for several years with no problem.
The oil cooler was installed on the firewall and the oil hoses to the engine were SS-braided. So the SS-braided hose worked as the engine ground strap.
To answer your question, the starter takes about 200-250 Amps.
Without a ground strap of sufficient size (2ga) this current will take an other path. It is highly likely that the large current could cause damage.
I would remove the inner wires of the throttle, mixture and propeller and inspect them visually. Some owner would replace the whole control wires.

Good luck

I installed two engine to airframe ground straps, ran the battery ground to the engine and installed at least four grounds for instruments and avionics to the engine.
The number one electrical problem is usually a bad ground, I admit I went overboard.

To answer the OP's question. Personally I can't imagine a way to inspect a control cable inside to confirm it has a problem.
If it works I wouldn't worry about it. They are pretty robust. I would get the ground on and go fly.
Art