I know what you mean. I don't use a console controller, but i also "handicap" my accuracy a bit by using a HOTAS. I also lost quite some accuracy early of the games lifetime, when i switched from keyboard and mouse to HOTAS. But at least for me, after just a few years of training, my accuracy is acceptable again. (I never will be as good as some other people posting videos here. What can i say, i'm an old man playing space fighter.

)
So i guess that also on a console controller you can get accurate enough with a bit of practice. For sure, the Eagle is a great choice there. You sure have to watch your back on the ship, as it's rather fragile, but it's excellent turn rate makes it much easier to keep fixed weapons on target than most other ships. So i think it's a good basis to learn using fixed weapons.
Yea. I also wish small ships would be of more imprtance again. But i also don't know how to do that. The idea of small-only missions, i just don't know how to do it. At some time, it would've made sense to have structures like from CQC in the game, with mission objectives somewhere inside the tunnels and the likes. So only a small ship could achieve the goal.
Unfortunately SLFs by now defeat the purpose. Instead of bringing a small ships, people would bring a large ship with high defenses and a SLF hangar. The elite rated NPC would keep the big ship alive, while people would rush in, do the small ship part in the SLF, then return to the big ship.
Thus i think the only way to make small ships viable again would require the ships themselves to be more competitive again. And at least in my perception the first step for that would require a significant nerf of the current stacking of defense. Which i unfortunately don't ever see happening.