Snubbers are generally needed for any circuit with a solid-state switch. I think one might be needed here, too. Here is my reasoning.
When the TRIAC switches off at zero current (or close to it) the tiny residual charge in the junction must be dumped. That may stimulate a parasitic oscillator formed from the capacitance and inductance of the wiring and switch, and thereby create ringing. The ringing's peak voltage may exceed the limits for the TRIAC junction and damage it, either one time or over time.
A snubber is inexpensive and easily fabricated. The snubber's capacitance must be greater than the parasitic capacitance, but it can't be too large or it increases power dissipation through the resistor from its own stored charge which has to be dissipated.
There's another issue. Switching an inductive load (power transformer primary) causes the voltage heading back to the mains to spike as the primary field collapses and is converted back into current. Without a flyback diodes to dissipate it, that energy must go somewhere, and the voltage climbs until current may flow. The destination is back into the TRIAC. Again, same problem with high voltage exceeding the junction limits.
Power transformers without snubbers also ring in normal operation, and that ringing can cause high-frequency spikes which may exceed the junction limits.
When the TRIAC switches off at zero current (or close to it) the tiny residual charge in the junction must be dumped. That may stimulate a parasitic oscillator formed from the capacitance and inductance of the wiring and switch, and thereby create ringing. The ringing's peak voltage may exceed the limits for the TRIAC junction and damage it, either one time or over time.
A snubber is inexpensive and easily fabricated. The snubber's capacitance must be greater than the parasitic capacitance, but it can't be too large or it increases power dissipation through the resistor from its own stored charge which has to be dissipated.
There's another issue. Switching an inductive load (power transformer primary) causes the voltage heading back to the mains to spike as the primary field collapses and is converted back into current. Without a flyback diodes to dissipate it, that energy must go somewhere, and the voltage climbs until current may flow. The destination is back into the TRIAC. Again, same problem with high voltage exceeding the junction limits.
Power transformers without snubbers also ring in normal operation, and that ringing can cause high-frequency spikes which may exceed the junction limits.