Can you get an "optionally cordless" or "hybrid" drill?
The main reason there is not a hybrid is the motor voltage. Corded drill use motors that run on 120 volts AC, (supplied by the grid). Cordless drills use motors that run on a lower voltage, usually between 12 and 18 volts DC (supplied by the batteries). A standard motor cannot run on both high voltage and low voltage. It also cannot run on both AC and DC.

To have a convertible or hybrid unit, it would have to run using a low voltage motor. There are three basic approaches to this that come to mind:


The unit could run on its batteries all the time. When the cord was attached, it would merely be charging the battery.  The problem with this is that the discharge rate is much higher than a safe charge rate, so all this gains you is a little longer runtime until the battery runs out. You would also get no increased torque.
The unit could run on the 120 volt AC voltage when plugged in, which would have to be both reduced to the lower voltage of the motor and would have to be converted to DC. This would require a serious transformer and circuitry that would add significant weight and bulk to the unit (that is what is in most of the brick type power supplies and battery chargers). The transformer would still be there when you went cordless.
It might be possible to build the transformer into a unit that plugs in like a battery and has a cord out the back end. But this would make the drill significantly heavier and bulkier than a conventional corded drill, a step backward in the evolution of tools.


The disadvantages to these approaches make it impractical. There also may be limitations that have to do with torque, speed, etc. for low voltage motors, but that is beyond my knowledge.