Neshkav, what you propose would eliminate being transgender from having any standing whatever as a medical condition that needs to be treated and put it squarely back in the realm of "lifestyle choices." It's taken years of struggle to begin to dent the attitude that gender-affirming surgery is medically necessary for some people, and it would be a tragedy if it were shoved back into the box of purely elective cosmetic surgery.
There are plenty of people for whom paying out of pocket even for safe, monitored hormone therapy will never be possible, and there are even more for whom paying for surgery is even more unattainable. This isn't any sort of moral failure or failure to "want it enough." It's the consequence of a truly effed-up social and economic system, in which things like race, class, education, and health status put vast numbers of people at a huge disadvantage.
It has taken a long time to get to the point we've now reached, where it's increasingly accepted that being transgender is a condition which, for many people, requires medical treatment and should therefore be covered by insurance. The problem is that the people qualified to give the medical treatment (surgeons, endocrinologists, and some primary care physicians) aren't qualified to make the diagnosis, which depends on psychological traits. This means that mental health professionals have to do that.
On the other hand, barriers to medical treatment, including financial ones, are among the major reasons trans folk suffer from psychological problems, with depression and self-harm, including suicide, among the most prevalent.
So, yes, treatment does need to be covered by insurance, and, no, gender dysphoria shouldn't be removed from the DSM. It's rational for insurers to want to be sure that treatment is actually needed, i.e. that this (or any other) condition is properly diagnosed, and this is the best mechanism we're likely to get.
To state the obvious, the reason some of us want gender id not to be in the DSM is that "mental disorders" in general are heavily stigmatized. Even those of us who should know better are scared by them; we often regard them as moral defects or personal failures rather than biologically based medical conditions -- which they actually are.
That is the basic problem here. By buying into the notion that ->-bleeped-<- shouldn't be in the DSM because "we're not like those people," we are contributing to their oppression. No one with any condition listed in the DSM deserves to be stigmatized for it.