With clones, I guess the official explanation is that natural-born troops were cheaper than clones, but I don't get why that same consideration wouldn't have also applied to the Old Republic. And is the official explanation of discontinuing use of battle droids that it was a basically a public relations move? Since when does the Empire care about their subjects' opinion? Apologies if this has been discussed ad nauseam.
In my opinion, it's not just that there isn't a clear reason to stop using clones, it's also that the movies at least never say that they stopped using them. I mean, if you're watching the movies in chronological order, you just assume that the stormtroopers are clones (because they're basically the same as the clones you saw in the previous movie). If you notice the different voices and heights you either assume they used different subjects as hosts, or just (more likely) that the producers had to use different extras/background actors. I know there's the whole TV/expanded universe, but for us who just watch the movies, stormtroopers are just clones (in the OT). (Also, the stormtroopers were indeed clones according to Lucas, for a long time - until he developed the life action TV series in the late 2000s!)
Natural born soldiers were cheaper but also take longer to train and organize. The clones were dropped in the Republics lap ready to fight hours prior to it was about to go to war. As for why the Empire would get rid of them? The clones are probably a bigger liability than they are an asset after order 66. Palpatine didn’t put all that work in just to get overthrown by somebody taking advantage of the same army he used to seize power in the first place.
The thing about hiring citizens to fight for your regime is gives them something to do that isn't fighting against your regime.
Clones age faster, so perhaps indoctrinating regular humans from childhood is the better way to insure more sophisticated troopery
Another thing to take into account is that a lot of the Stormtroopers were former members of their own planet's military forces that got absorbed into the Imperial military. So not only does the Empire try to ensure that new generations will join their military, but they try to ensure veterans of past militaries or conflicts will be loyal to the Empire as well. As for not using droids, I imagine it's a combination of it being potentially expensive (remember that the droid army in the PT era is seen as some top of the shelf stuff), and it would potentially inspire rebellion. In The Clone Wars we see that the Republic trained many anti-CIS rebel groups so if the Empire used battle droids that traumatized these guerilla warriors during the Clone Wars it would have just resulted in the proper Rebellion forming up earlier. Not only that but you would want to use these guerilla fighters in the Imperial military on harsh planets like Mimban to ensure that your government has a monopoly on these types of soldiers who would otherwise be a threat against a highly technologically advanced Imperial military.
Is there any information why the rebels never tried to use the armies of the trade federation? It would have made sense for the rebels to use those droids, right?
In canon the Rebels actually did use some old leftover Clone Wars resources from both sides. For example they used old AT-TEs and B2 Battle Droids in the mobile game Star Wars Commander. I wanna say some of the comics showed them using old stuff as well but I don't quite remember what it was.
Only if they had the means to build, supply and maintain them. I mean, Palpatine did have an override feature built into the clones. Whose to say there wouldn't be one for the droids as well? Maybe there is, maybe there isn't. Either way you can't 100% guarantee they aren't compromised in some capacity which makes them a liability.
I always believed because making normal humans being part of the Empire military will make the Galaxy to support the Empire more in Legends the Empire stop using Clones thanks to a Rebellion in Kamino i believe in Canon will be something about their Chips