Preheat-start ballasts exist which have integral starters. This means they have the typical four wires of an RS or TS ballast, but the characteristics of a preheat ballast. This seems to be more common for circline lamps for some reason. Here is a schematic I drew of what is likely inside these:
https://www.lighting-gallery.net/gallery/displayimage.php?album=lastup&cat=0&pos=0&pid=265862

Glow starters go bad. So much so that manufacturers felt the need to integrate them into the bases of some single-ended fluorescents to make replacement more simple. Because they go bad, they should be easily replaceable. This is usually facilitated by a socket that is accessible without fixture disassembly. So what did they choose to do with these integral-starter "self-start" ballasts? They potted the starter in tar, inside of a non-accessible component that is supposed to be a non-consumable, the ballast. Great idea.

I get that it is for space-saving purposes, especially for circline fixtures. But why didn't they just integrate the starter into the base of the circline lamp? What is the point of this buffoonery?

It is just abuse of nonexpert buyers, a result of predatory marketing and completely absent consumer protection.
A way to make the things really cheap even when that means it can barely survive a single lamp (as a failing lamp tends to kill the starter, that is the reason why both needs to be replaced together) and hide that from the customers.

Preheat-start ballasts exist which have integral starters. This means they have the typical four wires of an RS or TS ballast, but the characteristics of a preheat ballast. This seems to be more common for circline lamps for some reason. Here is a schematic I drew of what is likely inside these:
https://www.lighting-gallery.net/gallery/displayimage.php?album=lastup&cat=0&pos=0&pid=265862

Glow starters go bad. So much so that manufacturers felt the need to integrate them into the bases of some single-ended fluorescents to make replacement more simple. Because they go bad, they should be easily replaceable. This is usually facilitated by a socket that is accessible without fixture disassembly. So what did they choose to do with these integral-starter "self-start" ballasts? They potted the starter in tar, inside of a non-accessible component that is supposed to be a non-consumable, the ballast. Great idea.

I get that it is for space-saving purposes, especially for circline fixtures. But why didn't they just integrate the starter into the base of the circline lamp? What is the point of this buffoonery?

Sure the integrated potted part is just a glow-bottle starter and not some electronic circuitry?

In practice, unlike PL lamps deliberately made with a starter compartment in the base, there is *no* free space in the circline base. You can check by yourself, circline bases are usually easy to open by removing a single screw.

Circline lampholders typically compensate for this by adding a starter socket right near the lamp socket.

Some decent ballasts use way more long lasting starters (like thermal starters - a bimetal switch with heater connected in series with the working circuit, then way later indeed some form of electronic/FEC starters), but there really were products using regular glowbottle starter as a non replaceable component.
Have seen these not as ballasts, but as parts of light fixtures, those very cheap kitchen undercabinet T5 fluorescent lights, before the cheepeese electronic ballasts took over. These were really able to last only as long as the tube did.

Good glow starters in fact last a lot. And probably can outlast a few tubes if not abused by constantly blinking an EOL tube. BTW, at home there is a better possibility someone will notice an EOL tube timely and turn it off and replace quickly.

@Medved
I have heard of those fixtures with integral starters as well, similar idea.

@RRK
I never really considered that it might be anything other than a glow starter, but I suppose that is possible. That would certainly be better.

It is a real shame there isn't any free space inside circline lamps. Of course you could make them so that the base is bulkier (less tube, more base) but at that point it's too much effort.

You do have a point that EOL lamps are likely to be noticed faster in a residential environment. And even if the starter does go bad, the ballast isn't useless. Just needs an external starter (if you have space for it), then you are back in business.

I have somewhere one of those Medved mentioned. It is 13W T5, made by Osram in the 90s. IIRC besides the starter it had also a thermal fuse in the ballast, which might or might not have been single use (which would blow when the lamp stays EOL for a while)

 Many of our facilities were using Herman-Miller modular furniture. The cubicle has a desk and a shelf above. Snapped into the bottom of the shelf was a fixture to illuminate the desk. The fixture  used a F30T8 lamp and was equipped with a universal 202-S-TC-P ballast, the dash S indicating an internal starter. These ballasts had a very high failure rate after only a relatively short time.

Good glow starters in fact last a lot. And probably can outlast a few tubes if not abused by constantly blinking an EOL tube. BTW, at home there is a better possibility someone will notice an EOL tube timely and turn it off and replace quickly.

The problem is the starter gets overheated when the tube is degrading so the starter "just not trips yet". Problem is, the dissipation builds slowly and so does the starter temperature. But unlike during normal start (when the electrodes heat up so quickly the way more massive bulb stays cold before the lamp starts and the starter stops dissipating), with a worn out tube the thermal loading stays for rather long time, so the theat has plenty of time spreading over the whole starter bulb, so the whole thing gets very hot, All that while the fluorescent still appear lighting normally.
If the glowbottle is supposed to last long, there would need to be some kind of thermal cutout, responding to the starter bulb getting hot. That way the heat stress is stopped before that much excessive wear, so the starter then can last multiple bulbs. This is used in the classic format safety starters, which then are rated to last at least 3..5 lamps. But that cutout mechabism reliability is another can of worms, often failing on its own due to contact oxidation,.. But that would be way too expensive for such cheepeese products. Even with normal fluorescents the extra life of the curout starter won't cover the higher price, so they are used virtually only when there is another justification for them (like stopping the EOL lamp flashing,...).

My high school (built in the early 80s) used originally all 40W T12's with Prusman (Germany) metal can starters, no thermal cutout whatsoever

The starters were rarely replaced, they were kept many T12 and T8 tubes later. They would become progressively slow over the years, with some starters taking 20..30 seconds from switch on until any heating of cathodes / blink / sound from starter starts. But when they started, it was one long (5+ seconds glow in the ends of the tube) preheat and start at once, without blinking. So even when so old, they were still gentle on the tubes