as a non-American not familiar with how these structures work, is there a particular reason why these institutions are grouped by domain rather than by function, i.e. why so many branches seem to have their own intelligence agencies, rather than say, combine the intelligence agencies themselves? It seems very redundant and complicated to share information.
There a few different ways to slice your question, but one thing to consider is that there are very different "types" of intelligence "agencies/units".
If we use the broad definition of intelligence which might be something like "gathering and analyzing information to provide guidance to decision makers", and then label any group capable of information gathering and/or analysis as an "intelligence agency/unit", then you can see why they'd appear to proliferate everywhere.
Everyone with executive agency wants their own analysis capability. And everyone with executive agency probably wants their own gathering capabilities as well. And all for pretty reasonable seeming reasons. Technical specialization, time/latency/bandwidth considerations, risk tolerance. There are lots of reasonable reasons why specialization and localization makes sense.
Now the challenge obviously is to make sure you balance that against waste in resources, stuff getting lost in the shuffle, and straight up political infighting.
The US department of defense is the largest employer in the world, you have to have redundancies when you have nearly 3 million people working for you.
An independent intelligence service wouldn't have the interests of the other organizations it served. There are several independent intelligence services and military branches have their own. You want your intelligence service on your side and have separate services for separate missions so that priorities don't get mixed up and you don't have to get political to get what you need from some other organization.
It's not a matter of "this is too complex" but picking your poison as to the drawbacks of several different org structures.
Each branch is motivated to gather intelligence relevant to its operational plans. In the past there was a short-lived attempt to centralize US intelligence gathering (CIA), but the intelligence gathered wasn't useful to the actual business of running military operations, so now each branch of the military runs its own intelligence service.
Ultimately, the military is like any organization made up of people with the usual politics, interdepartmental turf battles, fiefdoms, etc. Sharing information means giving up "power" and, unfortunately, government employees are not selfless civil servants looking to make the world a better place (maybe on their best days they are), they are just people like us.
I don't think you're getting very good answers here, but the real answer is there is a split between strategic and tactical intelligence (and operational, but that's kind of in the weeds to distinguish from tactical). Military departments don't generally operate their own strategic intelligence assets. They get the information they need from the CIA, NSA, and NGA, the same as the president and anyone else who needs that level of information.
At the tactical level, though, military units need to be able to operate fairly autonomously. This can go pretty deep down. It means a division of the Army may have aerial recon assets, signals interception devices, and such with an operational range of, say, 500km or something, but not things like spy satellites that can cover the entire globe. Down at the company level, they may even have their own assigned scouts with some limited remote recon tech, but then the range will be much more limited. The point is they can use that stuff within their own area of operations without needing to deconflict with other users, having full local authority over tasking. Tasking of national strategic assets like spy satellites, on the other hand, needs to be done at a level of clearance and authority that has visibility into what all of the nation's military units are doing at any given time, as well as some idea of what they're going to be doing in the future.
This is why we have national intelligence agencies, but each branch of service and even individual combined arms units also have their own intelligence sections. It's similar to why local police departments have their own detectives and don't just ask the FBI to perform all investigative duties for them (more to it in law enforcement because there are also different laws at each level of government, but still some similar ideas).
Likely domain-specific knowledge for intelligence gathering. But there probably are also embedded human/political counter intelligence members from another intelligence agency to protect the branches.
Bureaucracy has a chain of command, and ultimately the people at the top of the pyramid only have the ability to focus on so much. That focus is partially driven by personal and organizational self interest.
It’s unlikely that the guy who runs the CIA will have the same priorities as the head of the Navy. Likewise, the Navy guy doesn’t care about tanks.
If it were a part of another agency it wouldn’t be able to prioritize issues the space force cares about. Its why the Army operates a sizable number of aircrafts.
