Guess what....alternators come in different sizes. Some of them such as the one in my Honda Element are quite small, just enough output to handle charging the starter battery and run the radio, the blower for the heater, the headlights and charge a cell phone. Likely it would charge a laptop too from a very small inverter but I would not do that if I had the headlights on. Running a crock pot for a lot of hours...no way, that would kill my small alternator and result in a very expensive repair bill. My alternator would not even handle charging a house battery that got drained down to 60% overnight. It might do it for a few times but it will before long destroy the alternator. If I want a house battery in my vehicle I would have to upgrade to a custom built, larger alternator and between the price of the alternator and installation I would be looking at close to a thousand dollars. It does not make economic sense to me.
Of course you also don't need an electric hot pot to have a hot meal at the end of the day. I just found a thrift store bargain, a non electric, thermal slow cooker that is made in Japan. Before you hit the road in the morning you start the ingredients on the stove top in the inner pot, bringing it to a boil then place that pot inside the stainless steel thermal pot and it slow cooks all day.
You can get yourself out of the mindset where you think all appliances need to be powered with electricity. Remember that there are alternatives out there, inventions from the past and also more recent inventions. Insulated thermal cooking is old technology that is being revived with newly made products and processes. Keywords to explore for those units "insulated thermal cooker" youtube and other places on the internet have lots of recipes and directions for using them.