I'm not very convinced about the usefulness of such an option.

For one, my guess is that this option in stk500.exe simply
predates the days of the EESAVE fuse, where each chip erase
involuntarily erased the EEPROM as well.

Second, why stop at a single byte?  What if someone wants to
read two bytes, or four bytes, or two times two bytes?  Or,
if someone wants to read the oscillator calibration fuse,
and store it automagically in EEPROM?

The same issue came already up with bug #17487, about how
to handle the oscillator calibration value.

So what I think is needed here would be a fairly generic
scheme "copy this many bytes from this memory space to that
many bytes of that memory space", where each option invokes
a new copy operation.  Unfortunately, this is going to be
a major effort which is beyond my own available capacity.
If someone wants to implement a complete functionality as
outlined here, please speak up on the avrdude-dev mailing
list, file a RFC for the implementation, and then start
implementing it.