State Alchemists in Fullmetal Alchemist are arguably the most powerful and knowledgable in the series, even compared to the likes of Izumi Curtis, who turned down the opportunity to become one when King Bradley offered her the position.
Aside from having unlimited access to most of the military's research on alchemy, they also receive huge sums of money to bankroll whatever personal research they might want to do. That being said, it seems that a lot of State Alchemists don't realize just how much power their position gives them, and most of them squandered the opportunity by the series' end.
10 Use Their Chemistry Knowledge For Medicine
As far as medical alchemy goes, it would appear that it is a very niche branch that not many alchemists undertake, let alone State Alchemists. The major exception to this is Marcoh, who was not only instrumental in the Elric brothers' discovering the truth about Philosopher's Stones but also in their creation in the first place.
It seems that, despite his vast knowledge of healing and the human body, as well as the standard chemical knowledge all alchemists have, Marcoh never tried to create any form of modern medicine, preferring to use his stolen Philosopher's Stone instead.
9 Further The Advancement Of Physics
In the same vein as the previous item, alchemists have to know a lot about physics to perform their transformations. They need to know precisely how much energy will be required for the transmutation to work, as well as the inner workings of various forms of natural energy in the case of Mustang.
It's questionable then, that throughout the series, the most advanced piece of technology was the Briggs tanks that Bradley annihilated during his assault on Central. With the kind of knowledge alchemists have, as well as their connection to the military, one would think they would have created some kind of flying machine by that point.
8 Research Alchemy
One of the major draws for civilians to become State Alchemists is the research grant given to them by the military, providing them almost every available resource and fund needed to develop their particular branch of alchemy. Over the course of the series, only one person actually conducted research for the purposes of military advancement: Shou Tucker.
Mustang completed his long before becoming a State Alchemist, Armstrong's brand was passed down through his family line, and Kimblee liked blowing stuff up too much to stop and think about what he was doing. Even the Elrics didn't do much research, they spent most of their time on the road chasing down other people's work.
7 Share Research
On the topic of research, as part of the conditions for working under them, State Alchemists are forced to share their research with the military, but no one ever shares their research with other State Alchemists.
For the most part, every alchemist shown working for the military uses their own unique form of alchemy, born from their own research, with the only exception being Armstrong. There's no restriction on alchemists sharing information between each other, so it's curious as to why they never do it.
6 Disobey The Military
One of the rules for becoming a State Alchemist is that members are forced under military rule, meaning if someone's orders are to travel to Ishval and murder everyone with fire, they better get on the next train.
Strangely, very few characters end up following this rule, and many alchemists either follow Father or Mustang, but not those in charge of the military itself. Even Ed and Al spend most of their free time doing what Bradley tells them, despite knowing who and what he really is.
5 Command Low Ranking Military
One of the perks that come with being a State Alchemist is holding the power and rank of a Major. Across the series, there isn't a single time when a civilian State Alchemist takes advantage of this power.
Of the few civilian State Alchemists shown in the series, none of them use their power as a Major equivalent to command members of the military. The closest instance of this happening is when Ed asks Ross and Brosh to keep quiet about their knowledge of human transmutation, and they don't even follow his orders for a whole episode.
4 Draw Transmutation Circles
Unless someone opens the door and sees the Truth, or has a Philosopher's Stone, they need to draw a transmutation circle to perform alchemy. Apparently, no State Alchemists got the memo, as every single one of them either uses tools that have a matrix carved into it or have one tattooed somewhere on the body, usually in the palms of their hands.
Even Shou Tucker, the supposed master of transmuting chimeras, has one permanently drawn on his laboratory floor. It makes sense from a time-saving standpoint, but it makes one wonder why standard alchemists even bother with chalk in the first place.
3 Command Civilians
As a military state, Amestrian soldiers have control over not only military actions, but civilians as well. Although viewers see many high ranking officials take advantage of their power, as well as people like Yoki abuse their power over the general population, no State Alchemists ever use this power for themselves.
For the most part, alchemists take their oath to be "for the people" very seriously, even those who have become dogs of the military.
2 Join Father's Cause
Despite the fact that Father requires human sacrifices to open Earth's gate of truth, no State Alchemist was chosen as part of the overall recruitment process.
The fact that a State Alchemist is bound to the word of the military makes this even more unbelievable. That not a single one either figured out what Father was up to and willingly joined him nor was anyone recruited by one of his many lackeys seems like a wasted opportunity by the writers. While technically Kimblee did work for the homunculi, he was never privy to the grand plan.
1 Kill King Bradley
As Ed pointed out by shoving a spear in King Bradley's face during his State Alchemy exam, the fact the latter was attending the event showed a major lack of security. Although Bradley swiftly destroys the weapon with ease, it does raise the question as to why no one else had tried to do the same thing.
Bradley and the Amestrian army had committed horrific crimes well before the Elric brothers found out what they were doing, particularly against the Ishvalan people. One would think that someone who had been at the helm of so much death would be in constant danger of being assassinated, particularly when surrounded by the most powerful alchemists in the country.