What i meant is, that the starting relays do have the option to use with capacitor start, exactly as you mentioned (that is possible but you have not seen it done)



The resistive start may be more reliable in terms of MTBF, but the problem is that nearly all failure modes of this method will lead to the starting winding being powered for extended time. It means that any failure of the starting mechanism has the potential to destroy the compressor

The PTC pellets tend to fail short circuited. Though i dont know what is the mechanism that causes the PTC pellet to fail in the 1st place - Is it result of wear of the material on the polycrystalline level ?

The electromagnetic relays will keep the start winding connected as long as the compressor doesn't start, which may be result of trying to restart into a pressurized system after a momentary drop of the power

I assume that in motors with winding for capacitor run, the winding has better chance to withstand external faults (short to the mains) for sufficient time until the overload relay (connected in series with the entire compressor load) shuts it down

With resistive start refrigerators is always an autoreset overcurren/thermal cutout. When start not suxessful, it disconnects the power to the compressor, waits for few minutes and then recloses back. This should be enough to the pressure to bleed off.
In fact the PTC starters are way worse offenders in failing to start and requiring the cutout to cycle: I haven't seen the system being pressurozed from normal runs to really prevent the compressor from starting (although I do not say it does not happen, mainly when e.g. the condenser is dirty), it may take a second longer but it started.
But attempted start with the PTC still hot (e.g. afterbrief power interrupt when the thing was running) is a guaranteed way to stress the compressor winding. And it does not matter it is the beefy power one, the current is to big extend dictated by the wire resistance, so wire stress by its length and voltage. And that is similar for both windings, the starting one isn't shorter, it is just way thinner and that way more resistive.
And when the compressor happens to need longer time for start, the PTC won't hold ON longer as the relay did, so it way more likely ends up in the failed start and stress from powering stalled motor till the cutout responds.
And if the cutout fails, it is way more likely to end by a house fire, as the PTC system needs the cutout to act way more often...

Won't the compressor body contain any hot/arcing parts of the motor, even if the cutout fails ?

Is there oxygen in the refrigerant loop which would enable ignition of the refrigerant inside the sealed system ?

The whole compressor body won' have that much difficulty to heat up to literal smoke, to the used oil selfigniting themperature. The current is in 15A ballpark, that means 3kW power. It may take some time, but there is not much preventing that. The internal electrical design won't have much issues maintaining the electrical integrity far above those critical temperatures, at least for the hour or so it takes to reach a point of selfignition.
The only thing it needs is something from the inside escaping out, like failed electrical feed through letting the presurized fill (with the mist of boiling oil in it) escape.

Supposedly the infamous Grenfell tower fire started from a faulty fridge, although there the main problem was the way how the fire spread after that, not what ignited it.