I'm baffled why this circuit is so widely used as an example of how to generate badly formed square waves. It really belongs in a Horowitz and Hill "Bad Circuits" section :-)
This circuit "generates badly formed square waves" when, as they say, the capacitor recovers its charge. For example, if in the OP's picture, Q5 is off, the capacitor C1 is charged by a current flowing through the path Vcc -> R1 -> C1 -> D1 -> the base-emitter junction of Q1 -> ground. Actually, this is an RC circuit... and the voltage across the capacitor changes in an exponential manner. The capacitor is connected in parallel to the collector-emitter part of Q5 thus determining its collector voltage... and this is the circuit output voltage with a bad form. In your case, this is not very important, because the collector resistor has a very low resistance and, moreover, you do not use the collector voltage an output. There are various ways to solve this problem, for example by connecting an emitter follower between the collector and the capacitor.
Fig. 1. A transistor multivibrator driving a reed relay through an emitter follower as a buffer (Young designer BG magazine, 1984)
However, there are applications in which this exponential form is desired... and I will give an interesting example from my practice - Fig. 1. In the early 80's, I came up with the idea to make an electronic compass using a reed relay powered by an AC voltage. This happened by accident - while experimenting with a device in the laboratory, I noticed that its behavior depends on its position (angle of rotation). ItThis voltage had to have a linear, sine or exponential shape with an amplitude very close to the moment of activation of the relay (I chose the exponential shape because the device was battery powered.). When the earth's magnetic field was added to this "AC bias" magnetic field, it began to "knock" and pulses were used to turn on an LED (this was a kind of PWM). Then I thought to use this circuit of a transistor multivibrator but with a "bad" shape of the output voltage. That is why the resistor R4 has so high resistance (68 k).
So in this case the "bad" was "good" for me (there is such an inventive principle)...