Corded tools are AC. Battery tools are DC. You'd need a converter which would be bulky.
But, I do think the Plug-It system is a great candidate for this type of solution and said as much when I worked at Festool.
Do you mean use a car battery and inverter with modified Plug-it cord?
Or maybe like the Mirka CEROS, where the sander is a Brushless DC, but the power supply is external rather than inside the tool like their later DEROS.
Then all the tools would use a common battery, and the power supply converts to DC and has a male end that goes into the battery slot... but instead of terminating at a battery it heads off to a wall outlet.
Or one plugs in a battery in if there is no wall outlet, or they wish to not be leashed by a cord... Basically they have a choice whether to charge a battery from the wall, or power the tool from the wall.