Cranking can pull hundreds of amps, if everything is robust enough getting House and Starter combined for the job can be helpful.
Yeah, that's part of what depends.
The starter on a 1GR-FE V6 Tacoma, 4Runner, FJ Cruiser is rated 1.4 kW and pulls around 125 amps worst case. The factory only uses something around a 6 AWG in the starter harness and gives people with stick shifts the option to bypass the clutch and start the truck in gear, which is a much worse case than just cranking the engine since you're literally driving the truck with the starter.
Compare that to a 8k lbs winch, which has a motor rated at more than twice and almost 3x that and those are delivered with harnesses with 2 AWG cable.
For a light duty truck or passenger car 4 AWG is completely adequate. I can let my 1GR-FE idle and still jump start most other passenger vehicles and voltage doesn't drop much. My alternator is rated 140 amps but at idle it's of course probably only doing half of that, so the reality is it's only taking maybe ~100 amps to actually start the engine.
Even the cheap 6 AWG Walmart specials are going to work fine for that (assuming continuous cranking, it'll take a 6 AWG cable 121 seconds to rise from 40°C ambient to 105°C with 125 amps), at least until you get into full size or commercial class trucks with diesels.
My point is whether 4 AWG is sufficient or not requires asking what's doing the jumping and what's being jumped.
All we know is it's "a van" and he's only asking about jumping starting someone else. Does he mean jumping a motorcycle he's carrying? Or the FMTV his traveling partner has? Does the van have dual 200 amp alternators on a diesel or just the stock single 150A on a base V8? Heck, who knows, maybe it's a mini van with a 4.3L V6 with an even smaller alternator.
If the argument is to minimize voltage drop, that's fine but a different criteria from strictly safety. I've upgraded all the starting and heavy charging cables in my truck to 1 AWG for that reason. Thick oil in the winter with a depressed battery, sure, you want to reduce losses where you can and heavy cables aren't going to hurt. The current the starter draws isn't going to be any greater than it's rating, though.
But I'd suggest that you may not even want large jumper cables to the point that voltage drop is very small. The dead battery won't draw significant current until the voltage on it exceeds roughly 13.5V (give or take). So if you have 15' (30 feet loop) 4 AWG jumper cables with your truck at idle of perhaps 14.6V the voltage drop at 125 amps is around 2V so the dead battery is only going to trickle and not add much load. You just need to make sure the dead battery end stays above about 10 or 11 volts at whatever current the starter requires to work.
If you make 1/0 AWG jumper cables then your charging system could start to really work along with trying to supply current to crank. The 30 foot loop drop for 0 AWG is about 0.75V at 125 amps so the dead battery is still seeing on the order of 13.8V with the source end at 14.6V and then it will draw whatever current you can source along with the load of the starter. Then you need to idle up or you risk significantly drawing down your own battery if you have to crank a lot.
Since he's concerned with his dual battery wiring, that's where you find the weak links, too, so sizing of all your wiring and fusing becomes critical. Or at least knowing to manually disconnect the undersized parts of the harness to protect them.
