there are a couple of reasons for using a wax motor:
- it's a thermal device - it will not release immediately upon power failure - that provides added safety in a consumer appliance.
- as pointed out by others, a simpler driver can be used (also, much less power)
- delayed operation is a safety feature also in this case.
- once the bad thermistors are removed (that were blowing the traics), it's a very reliable device - probably more so than a solenoid.
- it's cheaper than a solenoid (no copper coil)
I believe the dominant design consideration is #1
SNIP