I've been thinking about this a lot myself recently!
A few things I'd love to see:
Ground Attack Fighters
It's such a shame that iconic OG ships like the Sidewinder and Eagle so quickly become redundant. Sure, Elite Dangerous is a game where you can do whatever you want in whatever you want, but the Sidewinder and Eagle don't really have a (conventional) niche in which they excel above everything else. I think Odyssey offers a really good opportunity for a new lease of life though, as the "air support" component of the whole on foot sphere of combat thing. Providing the Eagle/Sidewinder with access to bombs that deal AOE damage, or maybe even laser-guided weapons that require the assistance of a player somehow (some kind of grenade/item for the on foot player that provides an object an airborne player can target with missiles/bombs/gimballed/etc) could add a fun new twist to combat, and by limiting them to ships like the Eagle or Sidewinder, you build in a little bit of automatic balance by restricting them to smaller/squishier ships. Maybe it would only be useful as a gimmick, but having someone lob a sticky grenade at an SRV, and then an Eagle swoop in to shoot off a couple of missiles at it feels like something that would open up some fun shenanigans.
Player-Deployed Soldiers
On foot combat zones already give us Vultures showing up and deploying soldiers. It doesn't seem like it would be much of a stretch for a similar functionality to become available to players: a module that lets you launch/spawn NPC soldiers to help out in a combat zone. Maybe it's a reskinned Planetary Vehicle Bay: the door opens up, and folks jump out of the bottom. Maybe it is more of a "bomb bay": an object is launched from your ship, and soldiers spawn from the location where it impacts. Maybe it works a bit like a limpet controller, and your ship needs to have passenger cabins (or a new "barracks" module, or whatever) instead of cargo to accomodate the "ammo" for your dropship module, adding a bit of build flexibility and creating a bit of a restock/resupply loop so that players can't spam reinforcements infinitely, but can also configure their ship to maximise the amount of cavalry they can send in. Limiting which ships can fit this module would be the way this brings new life to old/niche ships: the Federal Dropship, obviously, the Vulture, whichever of the Alliance C's gets the least love, etc. Paired with Ground Attack Fighters, it starts creating roles for spacecraft in Odyssey combat too, which I think would be a fun/needed incentive for players to bring ships along to that fight - and perhaps for NPCs to do the same, creating a need for things an anti-aircraft SRV and what-not in the future.
Larger Fighter Bay
While the Eagle and Imperial Eagle are quite big, the Sidewinder and the Hauler are not
that much bigger than the Ship-Launched Fighters we already have. Since the Condor and Imperial Fighter from CQC are already among the SLF options, having a version of the Sidewinder there would be a nice bit of parity if nothing else. But, if FDev were to add in a dismiss/recall feature similar to what we get in an SRV, that suddenly opens up a whole new functionality for "auxiliary" ships. Currently, the game can cope with your SRV having its own inventory, separate from the inventory of your ship, and you can transfer items in and out of that inventory using the existing UI. Add the same functionality to a Ship-Launched Hauler, paired with the ability to dismiss/recall your ship while in space, and you've unlocked a transfer vehicle. You've unlocked the ability to fly from A to B in a fully loaded Type 9, and then ferry the contents of your ship back and forth using a Hauler - similar to what commanders do already with Fleet Carriers. Is it a min/maxed way of doing it? Nah, grind for a Fleet Carrier or whatever. But it's cool, and suddenly you've got a reason to use a (ship-launched version of a) Hauler, to use/buy Hauler skins from the ARX store, etc.
It wouldn't necessarily just be helpful for cargo, either. In exchange for whatever tonnage the larger "Shuttlebay" occupies, you get the ability to use the (generally speaking) longer jump range of a bigger ship to get you to where you need to go, but then when you get there you've got access to something that can land on a small pad, or something small that can get closer to the ground to make finding Exobiology targets easier. Heck, even the sheer convenience of having a small/nimble ship with a cargo scoop that you can deploy to gather up salvage could be a nice thing to have. I'm sure there's more options that could be opened up by this framework as well - maybe some sort of deployable mining ship that does the lasering/abrasioning while the parent vessel does the limpeting? - and in the future, if we start getting planets where the atmosphere is significant enough for aerodynamics to start coming into play, the option to bring something like a Hauler or Sidewinder with you so that you can leave your Type 9 up in space feels like a good functionality for the game to have.
Asp Mk II (or Mk III)
Part of the lore with the Asp Explorer is that it's based on the Asp Mk II. This was designed for military/police work, and is basically the version of the Asp that appeared in the older games. The Asp Scout pretty heavily echoes the shape of that OG wireframe Asp from the original game, so my headcanon has always been that the Asp Scout is basically the Asp Mk II, but it's ex-military, stripped-down, nerfed for civilian consumption, etc - unlike the Asp Explorer, which was specifically designed as something changed/enhanced for the civilian market. This feels like a really good narrative excuse to buff the Asp Scout, because if it is the stripped-down version of the Mk II, presumably it can be "stripped up" and restored to military specs without needing to add a new ship/model to the game. FDev would probably need to be careful not to compromise the obscure niche that the Scout does occupy (it has it's fans, and IIRC it's not bad for cold running if you configure it right) - or add a new ship with an identical or subtly tweaked model, which I'm sure will make some folks cranky but w/e - but it feels like a really easy excuse, using that existing lore/history and the fact that there's a war going on to justify any tweaks. Cold running is pretty useful for AX combat as I understand it, so that seems like a pretty good niche/role to aim for with an improved "AspAX" as well.
Edit to add:
The Asp Scout, T-7, FAS, FGS are all largely redundant and need tuning. The Asp Scout needs the most love.
Fully agreed on the Type 7 needing some love. I know a few people stubbornly/defiantly use it for station rescue (it isn't the best for the job, but it's just begging to be a space ambulance), and I feel like that opens up an interesting point: could/should FDev be tweaking some of the less loved ships so they're better suited to these newer niche situations? Right now the smart move for station rescue seems to be "use the Python", and I'm wondering if/how things like the Type 7 could be tweaked to better suit roles that didn't exist when all these ships were initially created.