Yes they do have table saws that stop the blade once an electric circuit of sorts is completed by your finger/hand/whatever. And yes it would be great to still have your finger, but it also severely damages the saw, I believe it more or less ruins it. It damages a lot of internal components and shears something vital in the motor. But yes that may be a possibility for an electric/battery saw in the future. For a gas saw, that would have to be a different method since its set up a bit different.
Yes Skeans, your saws have tons of torque provided the clutch is tight and functioning properly, but if your clutch is shot, the chain doesn't move the same because it slips just like a car/truck. Chaps work to disrupt the clutch and bind it up with all the little strings and fibers in the chaps. Yes they also wrap around the chain and that helps also. With an electric saw, there isn't the same clutch setup, the motor is more direct drive so the fibers of the chaps have to rely on just wrapping up the chain, which isn't as effective. Now this is what "I remember" being explained to me when I was trained by Stihl about 25 years ago. Not sure about todays battery saws, but we were told that the electric saws then were more dangerous than gas because the chaps weren't as effective at slowing the chain. Of course sound mind should always be your first line of protection.
I say in my house, almost daily, "There is no substitute for safety or manners".