Peak Voltage Ratings of SMD Inductors
Good questions.
Answers are harder.

Voltage breakdown is closely related to manufacturing methods and materials and good answers require a manufacturer to provide information based on what they have done. This is less commonly provided, as you note.

Two physically apparently identical inductors may use differemt insulating materials and have differences in voltage breakdown of a factor of "several : 1". Double would be easily achieved and 5+ times might be seen.

The various questions you ask are all relevant - but also largely unanswerable without manufacturer cooperation. eg the question about rise time and breakdown MAY have an answer if all other factors were controlled, but other factors will easily swamp this in most cases.



One question you ask relates to a less known than should be aspect of some inductors.


  What is the temperature dependance of this possible breakdown ?
  Could a coil thermaly runaway and expire ingloriously?


It can be a temperature x time function and yes, some inductors can do just that, and do.
Of particular relevance are metal powder coils used for power conversion at high frequency. Coil mu and consequent inductance and frequency characteristics are affected by the powder material, grain sizes, and how much is used. These are taiolored by manufacturers to suit various needs and resu;ts vary widely. Active material is contained in a "binder" and then housed in an outer material - typically as toroids. While bottom end or 'clone' manufacturers provide minimal or (often) no data about the effects of temperature and time on these composite cores, competent manufacturers may provide detailed information. These can show the thermal rise in the core under various loading conditions and the lifetime expected under various temperature x time scenarios.
What typically happens is that therma aging of the binder leads to increased overall thermal losses which leads to higher temperatures which leads to higher losses which leads to ... .  Core thermal runaway is not something usually expected but that's what happens.
At one stage I was involved with designing a smps for a product manufactured in Taiwan. Long term thermal lifetime was an issue. I specified "micrometal" brand cores with specific instructions that genuine parts MUST be used - with explanations why. Micrometals colour code their cores wnd have trademarked the colour schemes. One can find a lot of cores with identical colour coding that are blatant visual and nominal electrical copies. The chances that the clone makers pay as much attention to long term core thermal performace is minimal.
  I was never 100% sure whether the not-too-bad rate of long term core failures was due to clone brand use, but it seemed so.