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There are alchemists, and then there are state alchemists, but what really is the difference? At the most fundamental one is a civilian and one is a member of the military. Both have access to some amount of incredible power that makes them more productive members of society than the average person. Seeing as those who pursue the title of State Alchemist are the most powerful individuals in this already elite class, what does it take for one of them to achieve the relatively exclusive title of “State Alchemist”? And given the difficulty in doing so and the harsh requirements to maintain that status, why would they want to achieve that title?
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Certification
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Candidates who seek to become State Alchemists must undergo a rigorous certification process that includes an extensive examination. The written test is designed to prove that they have a high aptitude for alchemy, generally within a specific field of alchemy but not necessarily.
They then must undergo a psychological examination that determines not only if the candidate is stable but also whether or not they can handle a military posting. This is an important portion of joining the military in this country and likely not exclusive to alchemists. It is however made clear that due to the specialized nature of their specific branch of the military that this test is fairly vigorous.
Candidates must then prove in the field that their specialized skill has a practical application that the military can both rely on and find useful. For some like the fire alchemist this is a simple task, for others who use their alchemy for research purposes this can be a daunting and psychologically harrowing task. Importantly, just because an alchemist initially proves useful does not guarantee their status for long. Every year a State Alchemist must present to the government their research and prove that they have made progress or shown success in order to renew their license.
Despite there being a requirement to submit research for license renewal some alchemists seem to be exempt. These are generally the alchemists who are actively serving in the military rather than engaging directly with research. Presumably, their military records serve as replacements for pedagogical reports, though this is not explicitly stated. Additionally, the King can himself simply renew a license without any assessment should he so choose, which he does in the case of Edward.
Requirements
Being a State Alchemist comes with strict requirements beyond the constant assessments. They must also follow three laws, although all three laws are arguably applicable to all alchemists. Firstly they must obey military commands and military hierarchy. This rule has them largely reviled by the general populace and has earned them the nickname “dogs of the military.” To this end, they must consider themselves tools of the government and may not use their alchemy for their own gain or influence, instead only as the military deems fit.
Secondly, they cannot create gold, this law does apply to all alchemists in an effort to protect the economy, but to State Alchemists especially. Should they break this law they face not only regular punishment but also military charges. Thirdly State alchemists, and all others, are forbidden to engage in Human Transmutation. This rule applies especially to State Alchemists since their skills and resources make them the most likely candidates for success.
Benefits
With such stringent requirements, popular disdain, and aggressive testing, why would an alchemist want to take on this role? Because most alchemists are at heart scientists, and with the State License that they receive they have access to nearly unlimited resources as well as all classified documents. To a scientist in pursuit of their ideas there can be no greater reward, and maintaining that status becomes of paramount importance.
Additionally, they receive a silver pocket watch as an emblem and the rank of Major in the army. This means that even a teen like Edward commands the respect and obedience of other high-ranking military officials, although his is an unusual case. Having received the rank of Major doesn't preclude them from rising higher but simply serves as a starting point. Tangentially with military power comes political influence, which to some State Alchemists is the ultimate goal. Instantly becoming a Major can be a quick way to jumpstart a career.
To become a State Alchemist an alchemist must undergo an assessment process that requires them to prove that they can contribute to the government's needs, generally in a unique way. Once they have obtained their license they then each year must re-establish their value. However, this tedious process comes with major benefits in regard to resources, and leeway regarding their personal pursuits. It’s clear why the most powerful alchemists view this as a valuable position despite the requirements and bureaucratic red tape involved.