so, what can drones do that fighters can't?
the answer, of course, is suicidal behavior, and melee attacks.
"Suicidal behavior," which I assume means "crashing into enemy ships to cause damage," just turns drones into a missile system. Not even a very good missile system if, as you suggest, the drones were to function by actually latching onto the target before doing whatever they did to damage the target, because if you require something to latch onto a target then it needs to impact the target slowly enough that the thing you're trying to attach isn't too badly damaged by the collision to function correctly, which implies an approach at low relative velocities. Which, in turn, means that your drone is, from the perspective of its target, an easy target for the target's point defense systems. Just use a real missile and be done with it already.
As far as "melee attacks" go, aren't things like Vulcan Cannons and Light Machine Guns short-ranged enough? Do we really need completely impractical weapon systems like the buzz droids of
Revenge of the Sith or the octopus things of
The Matrix, especially when the supposed "cool" factor of melee spaceships really isn't there since all we're likely to see is at most some blinking lights and small bumps on the surface of the target (consider how small drones and fighters become relative to even a small carrier like the Gemini when docking; even if the drones don't shrink when attaching to a target vessel, all you'd see is the drone sprite overlaid on top of the sprite of the target ship, maybe with some blinking around the borders of the drone sprite)? As far as the practicality of the system goes, cutting through armor-plated hull rapidly enough to be a useful attack in a battle is unlikely to be significantly less damaging than just blowing a hole in the hull with a standard weapon; cutting through armor-plated hull more slowly so as to avoid damaging high-value ship systems (to improve the salvage value or make it less expensive to put the vessel into service within your fleet) is unlikely to be fast enough to have an appreciable impact on the battle and as such would significantly increase both the risk to which your ships were exposed and the likelihood that the crews of the targeted vessels would be able to mount an effective response of some kind to the attack. Then there's the issue that a drone which not only needs to attach to the target but also function at a more complex level than "explode violently" suffers from being at least as easy a target for the point defenses of the ship being attacked as the suicide drone that for whatever reason has to latch onto its target before exploding.
the other thing you could probably make them is ablative shields. add a few "formations" for them (like line, wall, etc) and put them in front of their master ship as ablative armor.
It would seem to me that shield drones should have a reasonably high chance of blocking shots emanating from the drone carrier; unguided weapons fired by the drone carrier at nearby hostile ships have to follow more or less the same trajectories as those fired by nearby hostile ships attempting to shoot the drone carrier, and there's very little evidence in Starsector to support the idea that ships can coordinate shields well enough for the shots to not be blocked.
The Tempest can have up to seven weapons; two of them happen to be built-in IR Pulse Laser and Burst PD that can detach from the Tempest.
I think you mean five. Tempests only have three weapon mounts - two medium energy and one small missile. Regardless of how you outfit the Tempest, you're not going to have more than three weapons on the Tempest and another two on its drone. Those two medium mounts may be worth about as much as four small mounts, but they're still only one weapon each.
With very few exceptions, the ideal use of a drone system is to set it on free roam when the battle starts and then forget about it
I disagree. Most drone systems make for reasonably effective point defenses for the drone carrier if kept in the holding pattern, die quickly if allowed to roam free, and usually have a limited number of available replacements. The better use of most drone systems is therefore to allow the drone carrier to put something other than point defense weapons into its weapon mounts.
I personally feel that drones are fine the way they are.