Why (and how) flies fly like they fly

I was idly watching a housefly the other day - yes, a pandemic will do that to you! - and wondering why they fly like they do, i.e. jerkily, and apparently aimlessly and randomly.
First, a note about how flies fly. Most insects have two pairs of wings, which they move together in unison (in the case of bees and butterflies, the two pairs of wings are actually hooked together so that they move as one). True flies, though, have only two functional wings - they belong to the order diptera meaning two wings. The other pair of wings have shrunken over evolutionary time into two white drumstick-shaped organs called "halteres", which function as gyroscopes, measuring torque and angular momentum around the body. These halteres move in opposition (antiphase) to the front wings, attached mechanically to their respective wings, which is facinating to watch in slow motion.
Mechanically, video and modelling has shown that flies flap their wings over 200 times a second, generating enough force to move them and to react to changes extremely quickly, partly by flapping their wings in a way that creates something called a "leading edge vortex", a tornado-like phenomenon that creates enough force to stay in the air.
Why, though, do they fly in such an apparently erratic manner? This is mainly because they can only fly in straight lines, not curves, punctuated by rapid 90° turns called "saccades". They are not able to flap one wing faster or harder than the other in order to make turns, so they must roll their body to one side and pull up quickly, in a momentary spinning freefall, before re-engaging normal forward motion, rather like a fighter pilot in a high-G turn.
And their flight paths are far from random. They are actually an "optimal scale-free searching strategy". "Scale-free" in this context means that their flight path appears similar whether viewed up close or from a distance, like a fractal pattern. The searching, whether for food or mates, is also intermittent, in that they fly in (non-searching) straight lines and only re-engage search mode again every now and then when they make turns.
They are also making "on-the-fly" changes in direction to avoid crashing into objects and to avoid possible predators. Their small bodies, even their wings, are studded with sensors, and their complex eyes are simple but very efficient and give them an almost 360° view. Flies only have tiny brains composed of tiny neurons, but they do the limited number of things they are programmed to do very well and very quickly. If threatened with a fly-swatter, for example, a fly's brain calculates the location of the threat, works out an exit strategy, and position its legs or body ready for action, all with 100 milliseconds.
There is also evidence that flies also incorporate both visual cues and a sense of smell in their flight patterns. Furthermore, their apparently erratic and random flight paths actually follow a mathematical algorithm known as Lévy's distribution - kind of like sniffing, aseessing whether they are getting "warmer or colder", turn 90°, continue and repeat - which optimizes their chances of locating food or a mate.
So, it might all look pretty random and pointless, but there is a lot going on behind the scenes.
All of this, fascinating as it is, led me to one last question: do flies, and other tiny animals perceive time differently than we do? It seems like the smaller the beastie, the faster they do things (includimg reacting to fly swatters). Is that because time works differently for them? Do they see us as great lumbering hunks operating and moving incredible slowly?
Well, unlikely though it may seem, research suggests that they probably do. In fact, time perception appears to be directly related to size. The smaller an animal is, the faster its metabolic rate, and the slower time passes for it. Flies, for example, can perceive light flickering four times faster than we can.
So, there you go. Flies. Not just annoying pests. Well, mainly just annoying pests...