@Medved
A symmetrical multivibrator you pictured does not have problems starting even using silicon transistors. In practice, RC constants of base networks will always be slightly asymmetrical, enabling the circuit to start.
It is not that the circuit would stubborny refuse to start when powered ON, it is just not reliable, it requires sufficiently fast turn ON on the supply. And the reliability gets worse once the capacitors ESR increases or if the transistors have higher internal series base resistance (like most high beta transistors do, mainly important at higher currents) and/or the supply has no other source of noise/disturbance on it (sufficient fast ripple on the supply can restart the circuit from the deadlock, but then speeds up the oscillation)
It has nothing to do with symmetry. Try to ramp up the supply slowly, mainly with LEDs as the loads, and you get both transistors steady ON, whatever assymetry you have.
This circuit worked reliable with tubes, because even at the "both ON state" (with grids forward biased and anode voltages low) they had some gain greater than unity, so the circuit started to oscillate. But with silicon transistors featuring hard saturation the transistors lose all voltage gain, so no oscillation start.
Normally when trying it, you start with both capacitors at zero voltage, so when the power supply appears suddenly (rampup faster than time constants) the discharged capacitors do make a kind of bistable flip-flop with it which does select one state (which one depends on symmetry or random noise), where once one transistor becomes off for at least a brief moment kick starts the circuit.
But some brownout, or the supply not rising fast enough and the circuit stays in that "both ON" deadlock.
By the way there is a remedy for it: Do not tie the top end of the base resistors to the supply, but to a separate point, fed from collectors by two diodes. In that configuration when both transistors tend to go on at the same time, the top side of the base resistors loses power, so keeps transistors away from saturation. In that state they have plenty of gain, so the positive feedback via the capacitors amplifies the noise so much it starts to oscillate.
And once running, the top of those resistors get fed from the supply voltage present at the collector of the transistor that is at that moment off (neglecting the voltage drop across the liad). Because they alternate, the bases get supply all the time, so the thing keeps running normally.
But with these diodes we are not talking about the basic circuit anymore...