You say its a function of time then list 3 reason that are related to cycling which causes material fatigue. I'm scratching my head here.
TLDR: logically: the longer a heater accumulates "running hours" in a normal system, the more cycles it will undergo. h
********
Thermostats in mechanical heaters are comprised of bi-metal contacts with a gap in between. The size of the gap, or the tension holding the gap apart is set by the dial. As the temperature changes, the metal bends, eventually making contact. This cyclical motion is, by definition, causing "metal fatigue".
Logically - in any normally operating system where the heater can reach the set point, the more hours on the heater, the higher number of cycles that the thermostat will likely undergo.
Moreover, each cycle of the the contacts causes an electrical arc. These arcs degrade the contact points (flash heating, metal deposits and erosion and carbon tracking damage) that will eventually lead to failure if the metal fatigue does not come first.
Electronic thermostats are typically SCR controlled, typically with a few small filtering capacitors. If you want we can go into the failure mode of SCRs and capacitors, talking both about time based failures of capacitors, especially electrolytic, and the effect of cycling on SCRs and the filter caps.
Heating Element: Each time power is applied to the heating element, it thermally expands. When power is removed, it thermally contracts. This motion, by definition (thermal cycling) causes metal fatigue and will eventually create a weak spot in the element that will fail. Just like your electric stove element, hair dryer or anything else that has a resistive heating element. Logically (again) the longer the heater is in service in a normally operating system, the larger the number of thermal cycles it will undergo.
The seal between the outer shell (glass or plastic) and the end cap, cord seal, etc. Just like the rest of the heater, will undergo thermal expansion and contraction with each heat cycle. The materials will not only thermally expand and contract, but will do so at different rates because they are different materials. This will eventually weaken the seal between the two (glue or epoxy typically) that also undergoes the same process. Logically (again the longer the heater is in service in a normally operating system, the larger the number of thermal cycles it will undergo.
Heater failure is not caused by how old the heater is. If you read reviews they can fail after weeks and some have reported a heater running for 2 decades (you). You yourself list 3 reasons that have nothing to do with time.
Operating "time" is relevant to the number of cycles that a heater will undergo. It is not a direct metric and depends on the system, but for any reasonable system the longer the accumulated run time (or for that matter, time in service), the more thermal cycles that the heater will undergo.
Yes - some heaters fail in a week and some beat the odds by a long shot. There are numbers that we use to describe this. MTBF (Mean Time Before Failure). There are other metrics as well. For any given heater, those metrics could be calculated, but are surely not in this hobby and price point. They would be for military, commercial or industrial or aerospace equipment.
TIME ITSELF also changes some materials. Seals (say rubber, silicone, plastic etc.) and that too leads to eventual failure. Thermal cycling can (does) also speed the process. Basic materials science.
What is the point of recording runtime if there is no specified time a heater is good for?
That depends on one's goal I suppose. Record keeping to comparing failure times to predict future failures for the same model and/or plan for spares or statistical failure probability, etc.
Likewise, just because you (or anybody) does not have a need or the ability to apply those numbers or a reference (published MTBF spec for examples) to compare against, does not change the fact that the longer a heater is in service, the more likely it is to fail due to the reasons stated. It may be that simple intuition of planning says "Hey one way or the other, when my heater reaches 5,000 run time hours, I will proactively replace it"
Would a better metric to track be the number of cycles? Likely, but maybe the mechanism to do so is not exposed so the fallback would be run-time or time-in-service. Such fallback metrics are often used when more granular metrics are not exposed.