Okay, so the uploader of this video actually told me about the Ott-lite desk lamp that he has. Despite being electronic ballasted, it seemed to
operate the PL-S lamp with a starter, successfully, without any noticeable detrimental issues. Am I missing something?...
... unless maybe this desk lamp contains both an electronic ballast and magnetic ballast, which I highly doubt.
Anyways, here's the video: https://www.youtube.com/watch?v=eGQThMYJW14.

It is borderline okay, because usually a PL-S lamp has a capacitor inside (somewhere about 4700pf) *about* in the range of what to be expected for simple electronic ballast resonant capacitor. More, there are non-standard Asian 2-pin PL lamps containing a capacitor, but lacking a glowbottle inside.

 

The only problem with this is, the PL-S format does not specify the exact capacitor value or even its presence at all.
For magnetic the exact value does not matter and usually the starter works even with no capacitor, so some, mainly cheepeese, makers skipped the capacitor alltogether.
But the HF ballast needs the capacitor there unconditionally. It may be pretty tolerant towards its value, mainly when the glowbottle starter is present (it dictates the preheating current and OCV before the arc starts, but the glowbottle takes over the preheat when the capacitance is on the lower end), but if the capacitor is completely missing in some lamp, it won't work at all.
And because the standard does not strictly require the capacitor to be there, it needs to be formally restricted for systems where the missing capacitor won't matter, so to the mains frequency magnetic.