Detect open AC circuit and fire alarm
It looks like a good attempt but wont work because AC input to the power supply  has an unknown yet relatively high impedance compared to the 25W heater, so current will be limited.

It would be far better to ensure there are no air gaps in the heater tape to ensure solid thermal conductance to the metal pipes.  Otherwise self-heating and heater temp rise and failure will occur.  Hot pipes are usually insulated with slit foam tubing inside homes to reduce hot water losses. Something like this may also help.

I would expect pipe heaters to use high current (15A) with low voltage and then insulated pipes with insulated wire would operate at lower voltage and could withstand more gap tolerance.