Car starter motors and alternators are on a similar power level.

Definitely. The alternator on a small aviation engine (~100 HP) that I work with is rated for 24V/150A ~= 3.6kW and it’s not really that big in the whole scheme of things. The cables are about the thickness of my thumb.

I’ve wired a 3000W inverter into an RV, and the cables were a bit thicker than my thumbs. Use welding cable, it’s much more flexible.