I think a cordless drill and impact driver are essential, especially if you make a living with your tools. I agree with you about the batteries. They will be out of service long before the tool wears out. For larger tools, like you said, such as grinders and reciprocating saws, cordless are useless, in my situation.
Any time I pull out a recip saw, the batteries die, or overheat before I'm done. Same with the grinders. Then, I go get a cord, pull out the real grinder, and finish what I'm doing. My employer supplies all our power tools, so we all have large Dewalt 18v kits on our trucks. I will admit, the cordless grinder and recip are convenient when you just need to make a cut or two, but not worth it when you need a corded backup, too.
If I provided my own power tools, I would get a cordless drill, impact driver, light, and maybe the big impact wrench. Corded everything else.