Since nobody has actually answered HLS's original questions, I will try.

Thermosyphon (convection) in a modern engine could not work because
combustion temperatures are about 2,000 degrees, and the engine is meant
to operate at 194F. This excess heat must find its way, quickly, into
the cooling system. A thermosyphon system would operate far too slowly
for the heat generated to be removed before localized overheating
occurred.

As I said in an earlier message, with the thermostat closed, the water
pump constantly circulates and mixes the coolant in the block and head,
sending it round and round again, but ONLY within the engine so as to
minimize heat loss and promote rapid warmup. This keeps the temperature
even throughout the block and head. If you did not circulate the coolant
right from startup, you would risk localized overheating, boiling and
engine damage, even as outlying areas remained cold (including the
temperature sensor).

Thermosyphon is a far less efficient heat-transfer mechanism, since as
the surrounding water heated up, the rate of heat transfer from the
source would slow dramatically, and in any case would be far slower than
it would be under high-flow conditions. Also, the water pump's forced
flow provides the turbulence necessary to help disrupt any boundary
layer that may form and prevent efficient heat transfer.

Modern cooling systems use a high-flow, low thermal transfer
arrangement, taking advantage of the fact that greatest heat transfer
takes place at the largest temperature difference between source and
destination.

Finally, I'm not sure the water pump is much of a drain on engine power.
Or if it is, my guess is that there have already been steps taken to
reduce engine load as much as possible while maintaining necessary flow.
Emissions regs and CAFE would have seen to that.