Broadly, the long waits and the required letters associated with sex changes are intended to hedge against the risk of a "false positive." It is not a perfect process, but the system has a great deal of measures to protect against this type of error.
The problem with any process of timely operating on the correct set of individuals is that it relies on people having a high-level of intelligence, understanding, and integrity on issues concerning sex and gender. Society's proficiency on issues of sex and gender leave much to be desired, and this problem makes it difficult for people to understand SRS. When a conservative ideologue rails against TGs, GLBs, or even women wearing pants or holding positions of power, this misinforms susceptible individuals who hear the person's message (who will in kind misinform, bully, or otherwise cause problems for others) and diminishes society's grasp on how sex and gender operate. When cliques dictate behavior on the basis of sex or gender, or anything, regardless of their cis/trans numbers, they diminish society's grasp on how sex and gender operate. Doctors, psychologists, therapists, and psychiatrists all have varying professional levels of comprehension of how sex/gender work and have their own morality, personal beliefs, prejudices, and self-interests, and the extent these matters corrupt their work can interfere with properly referring, diagnosing, and informing patients. Media, family, friends, schools, churches, businesses, these all propagate flawed information. In total, people in society are bombarded with information -- much of it is (broadly) destructive, much of it is (broadly) constructive, and a good deal of it has to be untangled from the context it comes from. Even among allies, they are typically not exposed to the robust variety of individuals like we have on these boards to polish their understanding, and not even all of us can represent the entire set of possibilities or experiences.
The battle we have is to get to high-quality information, and to have that available to the masses. If the dominant narratives (just as an example) are "SRS is immoral and should never be done" and "anyone who wants SRS should be able to get it right away," then we're going to have trouble because we have to reject *both* viewpoints. Granted, one of these ideas is worse than the other, but neither is a real solution. Furthermore, we have to *replace* these narratives with one of our own. Doing so is complicated, because we may not know precisely what we think is right, and it is tricky to find other individuals who recognize that the issue of SRS cannot viewed through a duality. SRS must be available, but candidates for it must go through an educational process to make sure that SRS is right for them (rather than some elusive third/fourth/etc option that may not be obvious at first). Because as most of us know, in a world that still perpetuates the idea of pink for baby girls and blue for baby boys, a genetic boy liking pink does not translate to this person being gay, a girl (for whom SRS may or may not be appropriate), a "sissy," a crossdresser, genderqueer, third/alternate gender, or a "tough guy" -- it just means the kid likes pink. But it's not just enough for us to know every little bit like this so we can cut through the noise and understand what is true about ourselves -- we need the whole world to have access to this piece of useful information (sadly, this *does* to qualify as "useful" given present circumstances), and to every other relevant bit we can come up with. Because when you get down to it, we want precisely the right group of people to get SRS, keeping away those who would not benefit (and especially those who would be harmed), and granting it to those for whom it is part of an ideal solution. It is a difficult task, it will be riddled with mistakes (probably more often on the side of caution), and everyone involved will have to work to improve the system, but it is a worthwhile effort.
Quite relevantly, Susan's is an excellent resource for helping people settle in to the right identity and goals (if possible), making it less likely they make a decision they regret. Between the Wiki and the variety of identity-based message boards, lots of relevant information and testimony is available, people can see a great variety of what is possible, and curious individuals can interact with other users for more information. A person who first identifies as a TS and seeks SRS can see the possibility of being a non-op TS or an androgyne (and consider if such a plan/identity is better for them) -- we won't (better not) try to talk someone out of being a SRS-seeking TS, but we show many things that are possible (in case something else is a better fit), and we won't (better not) railroad a questioning person into a certain identity (like a TS who needs SRS). We are not professionals on the matter (although there are some exceptions), and we definitely are not perfect, but using this website or a comparable high-level resource is a great way to help make better assessments about one's identity and to help us better understand the identities of others (including not rushing to conclusions/stereotypes). It seems kind of cheap to say "this site is awesome and helps solve trans-related problems," but that is what Susan's does. We rock.