Does a phase-controlled dimming degrade the lifetime of filament or heater element?
There is going to be some stress every time the temperature changes.  Small fillaments might be able to change temperature significatly enough over half a line cycle so that phase-dimming might matter, although in most cases it is probably not a large effect.  If you are asking about a "heater", then presumably the thermal time constant is much much longer than a power line cycle, so there would be no harm to them due to phase control dimming.

The issue with phase control dimming is the nasty power factor is presents back to the power source and interference it can radiate and conduct back onto the power line.

 

For example, look at this waveform (in red) of a phase-control dimmer set to 60V. Notice how rapidly it rises- indicating that the waveform contains very high-frequency harmonics which will radiate out from the power lines, potentially interfering with sensitive circuits. 

Both these are real issues, and reasons why you don't see phase control dimming much anymore.  Good riddance.