Here's what I've heard about this issue: when you jump start someone, your vehicle should be running so that the alternator is doing the heavy lifting. With a hybrid, there is no alternator and the charger has a very small capacity. Since the 12v battery is not used to run a starter motor, it is not drained as much and does not need a powerful charger supply. So if you use a hybrid to jump somebody else, you are putting a heavy drain on a system that was not designed to supply a high-amp load, and running the gas engine doesn't really help.
I've heard some horror stories about jumping people even with a gas engine. Modern cars have way more electronic systems than older cars and they are not always very robust. Some people report permanent damage to the infotainment system after jumping someone, for example.
A few months ago I bought the "autowit SuperCap 2", and within a few weeks had multiple chances to use it. It's an awesome device and I plan to get another one for my Maverick. I'll use it to jump start others that need it and to jump my own vehicles if they need it. It's different than the battery pack chargers because you don't
I agree that some of the compact jump starters work very well. I have one and it works better than I ever would have expected.
But, there are a lot of misconceptions in your post.
A modern 'normal' car starter typically draws around 300amps when starting to crank and somewhere around 250amps to maintain cranking. A typical alternator can only produce about 100amps at full load. These are generalizations and figures car to car will vary. D point is, there are not any standard equipped non hybrid vehicles which have a standard alternator with enough output to crank over a starter. Largest output alternators I've ever seen were on limousines and competition audio rigs..... They maybe could do it.
The reason you want to start the car is so that the jumper vehicle puts a little charge into the stranded vehicles battery, maintains the starting vehicles battery a bit, and when running, the voltage in the system typically increases to around 14volts which helps give a little extra kick (and why 24v starting systems used to be a thing. Makes the starter spin twice as fast as long as there is sufficient current/amps available.) But without enough available current (from the battery) the 14v still wouldn't start the vehicle; that starter needs current flow, lots of it. The alternator can't supply it all at once.
The alternator only does the heavy lifting if you allow the vehicles to maintain connection for a longer period of time in order to charge the stranded vehicles battery, allowing it to dump current, which is not a bad idea.
In the cold, the need for amps is increased.
If there are no other underlying problems and the jumpers are connected properly, there should be no issues jumping a 12v system with another 12v system.
Sorry, not meaning to get into a whole electrical theory discussion here. I could go into a lot more detail (no ohm's law discussions, I swear!) but I'm sure many are already bored or are clinging to their own theories. I'm also sure there are others who could explain it better.