Hard Science Space Warfare
Christian makes a very strong point regarding those assumptions. Even the hardest science fiction goes in with certain assumptions that shape the universe, and one could even define science fiction by how it expands from such premises - if the assumption is taken to be true, we can expect the rest to logically follow. That is what we are trying to do with Starfighter Inc, and there’s a lot behind the scenes, as he deduced.
Out of universe, you could probably guess the reason we’re using manned fighters - Burnside’s zeroth law, people emphasize more with people than machines, and we thought it would increase immersion. We were willing to go to extreme lengths to make this happen. Early on, SFI was to be set in an alternate universe where computers developed much more slowly and so there was no alternative but for ships to be manned (this was partially in tribute to the golden age of science fiction), and for a while, we debated going the other way entirely and having pilots download themselves into their ship computers so you could pilot an “autonomous” drone and still be human. However, in both cases the technological implications caught up with us, so we decided to stick with a simpler setup. As for why manned fighters are used in our universe, there are three reasons.
Firstly, while you could just throw missile after missile, the greater the distance that the missile has to cross, the less likely it is to make it to the target. Between the target’s movement and its ability to evade, the time available for the missiles to be stopped by countermeasures or point defense systems. There’s a lot more involved than this, though; ships have a much easier time outrunning missiles because most missiles in-setting use chemical drives, whereas the ships use solid and gas core nuclear drives. What this means is that the missiles have much higher acceleration and are nearly impossible to outrun at close range, but the ships’ exponentially greater fuel efficiency lets them run for much longer and burn out the missiles in long pursuits. You could make a missile with a nuclear drive, but that’s a lot of money to throw away for an expendable munition, and at that point you’ve already got the basis of a drone or starfighter - just strap on a power system, ammo rack and gun, and now you’ve got a working platform that can be recovered. As for why manned fighters dominate over drones, that’s covered in the following two reasons.
Secondly, the universe is dominated by corporations which don’t really place much value on human life, and between this and the starfighters lacking onboard life support (the pilot depends on his spacesuit), there’s not as much difference between manned and unmanned ships as might be expected. That’s not to deny the difference in potential performance due to limitations imposed by said sack of meat in the seat, but there comes the third reason - one which Christian already guessed.
Thirdly, EMP technology and distance-hacking is in very wide use in-setting, neither of which is a concern to a flesh and bones pilot, so at the very least said sack of meat can serve as a failsafe. Most of the time. The “human element” isn’t always reliable, either.
As for why they fight at close ranges, that's partially an artifact of the setup of the video - the gaps in the rings of Saturn are less than tens of kilometers across in some parts, half that if you consider shepherd moons and asteroids in-between. But there are strategic reasons as well. Simply put, starfighters do better at close range, because nearly all of their weapons are more likely to do damage. Missiles can get the jump on nearby ships and there’s less time for them to be taken out, kinetic weapons are unlikely to hit at a great distance due to the relative velocity of projectiles to the ships and movement lag, and lasers have difficulty focusing past a few hundred kilometers taking away their potential destructiveness.
There’s not much that can be done about the missiles, but for the rest it turns out the solution is to go bigger. Longer mass drivers can accelerate the projectile for longer and hence reach higher speeds, and larger laser lenses can focus light to greater distances. However, there’s a pretty big snag, in that the effects are not linear, but quadratic. If you assume uniform acceleration throughout the barrel (which is _not_ true - acceleration actually decreases towards the end, meaning the reality is worse than this), time and hence velocity scale to the square root of length, so you need to quadruple gun length in order to double the speed. Similarly, kinetic energy scales to the square of velocity, so power scales rapidly, too. For lasers, the focusing distance is proportional to the diameter of the lens, but mass increases to the square of diameter due to the increased area. Suffice to say, increasing range for either of these weapon types is a weighty proposition.
To support weapons suited for many thousand kilometer ranges, you need capital ships. These are also easier to fight at range due to their greater cross-sections and slower response times (between the scaling of thrust, moment of inertia and simply the high centrifugal forces in crewed vessels if they try to spin too fast), but they have a few notable caveats relative to fighters. For one, every capital ship taken out is a huge investment of resources and losing even one can be a hit to any war effort, whereas you could build a thousand starfighters for the same price and afford to lose a few.
Nuclear weapons are what tilt the scale here - it is possible for a starfighter to eliminate (or at least cripple) a capital ship with a sufficiently high yield bomb, but the same mass of starfighters can disperse sufficiently to require a whole fleet of missiles. For another, the square cube law works against larger ships, at least if you assume that power consumption scales up directly with ship volume (when most power systems have slightly better specific power as they get bigger).
This is because the surface area that lets the ship radiate waste heat increases more slowly than power - scale up a ship tenfold, its mass and power should increase a thousandfold, but with only a hundred times the radiative area, it’s got a tenth the relative area - requiring much larger radiators that can easily make up the greater part of the ship, presenting a huge vulnerable area. On the other hand, the reverse scaling means that starfighters can get away with very small radiators and, in some cases (actually, all the ships currently shown), if run hot enough they can suffice with using their skin in this manner. Furthermore, the much smaller scale means fighters could potentially rely on highly thermally conductive materials for a solid state heat management system, making these systems much less maintenance intensive and much more durable than a capital ships’ fluid coolant loops and mass of pumps.
But there’s a third factor that’s more pertinent in setting, which is simply the implications of owning a capital ship at all. The megacorps are not engaged in open warfare, but are mostly squabbling under the table, sabotaging each other and trying to keep their squabbles away from the public eye. Insofar as nothing is really invisible in space, all they can do is control the information. Minor skirmishes between starfighters can be excused, and a carrier can ostensibly be used for civilian purposes, but a battleship means a new scale of engagement however you look at it, and raises questions and concerns the megacorps would really rather they didn’t have to answer (besides that, they’d rather not waste themselves in a full-on campaign).
That’s our setting in a nutshell. It’s a little difficult to translate to a four minute video.