How did you conclude that they aren't the most reliable long-term?
Temperature sensing is extremely simple and cheap. Bi-metal contacts have been used since the dawn of electronics, and the solid state versions are also really simple. (Making components that are temperature invariant is the hard task.)
Fair question! My speculation here comes from thermistors being relatively common replacement parts. (clothes dryers, ovens) As you mentioned, temperature-invariant is tricky, and I think it's often a non-linear but close-enough for the design. I have the impression a failure mode can be if the temperature-response behavior changes over time.
A bi-metal contact is only good for a single temperature, I think? (can be adjustable like thermostats) (I'm sure many but not all dish-washers probably do only need a single temperature...)
Temperature sensing is extremely simple and cheap. Bi-metal contacts have been used since the dawn of electronics, and the solid state versions are also really simple. (Making components that are temperature invariant is the hard task.)