No argument intended: yes, you can use switching transistors, but they
do consume a bit of power which they translate into heat which must be
dissipated. Switch contacts are largely loss less, but relays do
consume power, although I'd venture to guess that it is less than is
dissipated in switching transistors.

Actually MOSFET power transistors are readily available with 0.01 ohm of on
resistance, no junction drops and only microwatts required to drive the gate.
They would consume less power than the wires to the pump do -- very nearly as
little as the mercury switch does.

Using them would just cost more to build however and the manufacturers
apparently don't think they successfully could charge more for a more
reliable pump switch.

Sigh....

Bill -- (Remove KILLSPAM from my address to use it)