Why would my battery on a 66 impala be dead after driving the car all day with no problem cranking?

Batteries sometimes do that. I had one car battery and one motorcycle battery do it. The bike battery read 12 volts until any load was put on it. Couldn't even push start it. I guess they came apart inside.

The plates get warped and/or the electrolytes become contaminated, or a regulator has overcharged it...do you detect an unpleasant odor? If so, it's trash, it probably is anyway

could be from a bad generator and or regulator. these cars have a separate regulator ,usually locatated on the fire wall.

If the regulator has gone bad no charge reaches the battery and it goes dead, that happened to me on my '71, it should be located on the firewall or they also hid them behind the driverside headlight.