Well you can actually use a car battery to weld. You can also daisy chain them together and get better performance out of the setup. As in, if you chain several together you can use the setup to weld just about anything that is not a 2 inch bulkhead on a sail boat. You can also do serious welding with a tesla car without a doubt, seeing as the battery system runs the entire vehicle. You can most certainly weld 100% off of batteries.
^^ if you daisy chain a few together you can do serious work. Big tesla banks can do serious work. Proof is all over the net. Try google.
As for a forge. If you install a blower fan vent in the vehicle and use insulation, a forge can be perfectly capable of being inside an enclosed space. Hot, yes. But not kill the occupant hot while using ventilation. Even opening all the doors and windows would be enough if insulated. You can make a coffee can forge using a handheld propane tank. How do you people nay saying think you use a stove in your house without burning the building down? A standard home stove can be touched without harm over 600F. Using a blower(even a hair dryer) inside a forge using propane or other gas will provide heat enough to work steel.
The point is not to prevent people from having such a mobile base with such tools. It is a question of how do we change the silly game mechanics as they stand to better fit the reality of having such tools to work with. Youtube is not just anecdotal either. They have good examples of many things proving both electric/gas welding and forging can be inside a small vehicle. Not just a huge honkin flat bed either.
Focus should be on insulation, ventilation and blowers to enhance the heat while venting it.