Tow planes and gliders routinely fly with a disconnecting cable between two aircraft, and that seems at least as impractical and unsafe (or it would if you were proposing it as a new idea). Though maybe that's the sort of thing that's "grandfathered in" from earlier, more permissive days of experimental aviation.
I think the strongest argument against using a power cable during takeoff is just that it's not worth the effort and complexity just for a slight increase in range, except in rare situations or planes that normally make very short flights and don't want to be weighed down with extra batteries (like the aforementioned glider tow planes).
> Tow planes and gliders routinely fly with a disconnecting cable between two aircraft
This is true. However, the cable is not carrying KW or megawatts of electricity, it's just there for tension, to transfer forces from something else to get the glider airborne.
Technically, you don't even need the tow plane, some places perform winch launches (or car launches!) exclusively. This is very common where general aviation is not as common.
Should the cable not detach (extremely rare), it can be cut at the other end. Cutting a live cable should be much more interesting. Other issues, the glider can release it. The glider will most likely be fine, even if the flight is now cut short.
Gliders are very light and still the cable weights a lot. That's probably the limit of what's practical. There are some gliders with electric motors, they don't need all that much power, by definition. Some can even self-launch.
> Tow planes and gliders routinely fly with a disconnecting cable between two aircraft, and that seems at least as impractical and unsafe (or it would if you were proposing it as a new idea). Though maybe that's the sort of thing that's "grandfathered in" from earlier, more permissive days of experimental aviation.
A tow cable does not have live electrical conductors in it.
I think the strongest argument against using a power cable during takeoff is just that it's not worth the effort and complexity just for a slight increase in range, except in rare situations or planes that normally make very short flights and don't want to be weighed down with extra batteries (like the aforementioned glider tow planes).