Failure to take countermeasures against back EMF will significantly shorten the life of the circuit.
Left - No countermeasures
Center-Measures using diodes
Right - Countermeasure using snubber circuit
The diode solution is easy to use, but it cannot reverse the voltage across the coil.
If you want to take advantage of the EXOR-like characteristics of the relay, I recommend using a snubber or a circuit.