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.

I did an experiment a while back, using a philips programmed start electronic ballast on pl-s 9w and 11w lamps. The ballast specified it can be used with those (out of 4 pins, only 2 should be connected). The lamps worked, and some even started with a starter 'ping' just like a magnetic ballast. I put an eol lamp, and it flickered as if it was on a magnetic ballast. After 10 seconds the ballast turned off (eol protection)


So an electronic ballast is able to run a standard pl-s lamp with a glow bottle starter.

@LightsAreBright27, did your 9w and 11w PL-S lamps contain capacitors near the glow bottle? (Really interested in that 11w one as well, since
it appears we do not have 11w PL-S lamps here in the U.S.)
Also, when you say the EOL lamp flickered, do you mean flashed?
I would think that an EOL PL-S lamp, at least on a non EOL protected electronic ballast, would be extremely hard on the electronic ballast to
the point of ballast EOL.
... but what was the point of adding a capacitor near the glow switch bottle on PL-S lamps? I know now from you guys, @RRK and @Medved, that those
capacitors can enable use with certain electronic ballasts, but do they not help in terms of performance on the magnetic Preheat ballast?
Why add a capacitor for the starter based PL-S lamp if it's not required?