Why are there no (automatic) rear turrets on the X-Wing and Y-Wing?

I am not familiar with any model X-Wing having rear turrets, let alone manned ones, nor appearing in Episodes I-III.

As for the Y-Wings, I assume you are referring to the BTL-B "Republic" Y-Wing, as seen here (can be missing the panelling, which has other lore reasons I won't go into here):

We can see that, like you stated, there's a bubble with space for a living gunner, instead of it being controlled by for instance an astromech, targeting computer or the pilot themselves. The benefit of a wide bubble like this was that the gunner could easily see around him, while the seat and turret could turn a full 360 degrees around.

However, there were many downsides too, as one could imagine. Firstly, such a bubble exposes the gunner greatly to enemy fire. And as Legends has stated, at first, a shot to the canopy would mean the whole cockpit got sucked out. This later got fixed by separating the space of the turret and the pilot space (see Incredible Cross-Sections of Star Wars: the Ultimate Guide to Star Wars Vehicles and Spacecraft). But yet, the issue of the gunner easily getting shot out remained. This meant the gunner had to be moved somewhere more safe and concealed. This led to the development of the BTL-S3 and later series of Y-Wings, the ones you refer to when speaking about Episodes IV-VI.

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Throughout the whole of Star Wars, guns like these are usually controlled by someone other than the pilot simply for the reason it'd make things too complicated for the pilot, who's already under a lot of strain during combat. So, there's an external party needed to help. The Republic solved this by means of another clone in the bubble. This also has to do with the fact that at this point, it is implied astro mechs are not advanced enough to do both hyperspace planning and co-piloting as well as controlling such systems.

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Here we see a Y-Wing (either BTL-S3 or BTL-A4) during the trench run. You can see the gunner bubble is gone, yet I can assure you that there's still very much a gunner present (in most cases). But instead of being in an obvious, easy to shoot bubble, they are in the back of the canopy, under the turret. In Star Wars, humans are simply more trusted with targeting and shooting targets than computers (besides tracking assistance systems).

"The BTL-S3 was a variant of the Y-wing starfighter line. It was typically crewed by a pilot and gunner, who sat back-to-back in the cockpit." - Wookieepedia, excerpt from BTL-S3 Y-Wing

However, at this point of the Star Wars timeline, these targeting computers and astromechs have gotten much more advanced. So we start to see the gunner being removed, and instead the astromech controls the turret, or there's a targeting computer placed under the turret (although this was rare because of the aforementioned reasons).

Additionally, there was also the BTL-A4 Y-Wing which completely removed the gunner seat and instead locked the overhead cannons into an forward aiming position (sometimes in different archs, or other angles), so that the pilot could just pull the trigger at what he was flying at.

"The Koensayr BTL-A4 Y-wing starfighter was crewed by a single pilot. The 16-meter-long attack starfighter had an ArMek SW-4 ion cannon turret which was preset to one of four arcs and was typically locked forward, although some pilots chose to lock it facing aft for extra cover." - Wookieepedia, excerpt from BLT-A4 Y-Wing

BTL-A4 Y-Wing as found in *Oncredible Cross-Sections of Star Wars: the Ultimate Guide to Star Wars Vehicles and Spacecraft* shows the removed gunner seat, instead filled with electronics (probably retrofitted to improve other systems or allow for a bigger targeting computer, although there are no details on this). The texts on the page also back up the information I've been talking about about the BTL-S3 and BTL-A4 models.

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Here is my speculation on why Star Wars relies heavily on traditional army place configurations (a.k.a. any gun not pointing forward is controlled by an added gunner(s)): Star wars was first conceived during the late 1900's. It was also heavily inspired by World War II (see 'Historical')** when it comes to the warfare. At this time, the idea of such advanced computers in such a small package, or that are able to distinguish and attack 'enemies' was simply not thought of. Although, droids do exist, so do many other computers doing all sorts of stuff like this. So the only other reason I can think of is because Lucas simply wanted to keep to tradition of planes with multiple crew, possibly to keep it somewhat recognisable for the viewers.

"The space battles in A New Hope were based on filmed World War I and World War II dogfights." - Wikipedia, excerpt from Star Wars sources, Historical**

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** From Empire of Dreams: the Story of the Star Wars Trilogy (2004, IMDb). In this documentary, George Lucas speaks about the inspirations behind Star Wars' technology, clothing, but also the way fights are orchistrated and what vehicles are based on, amongst much more.