You raise a very interesting point, and one I've personally thought a lot about.
I'm not sure what gender I identify with yet, I'm still working that out. However I often feel dysphoria, which is a common trait among trans individuals. I was assigned male at birth, but I don't feel comfortable with the way people interact with me when I present as male. I believe it's somewhat a misconception that trans people feel like a woman in a man's body or vice versa, as I and many other trans people I know well don't feel that way.
HOWEVER having said that, you're definitely right about the operations etc. Resources should be prioritized to people that need them for deformations and life threatening illnesses. (Although debatably, denying a trans individual a means to accept themselves and connect with their outward image/experiences can be fatal, in many cases)
As I said earlier, I believe the real problem many people face isn't being trapped in the wrong body, but being trapped in other peoples preconceptions of them, which have been built up by capitalist money-making schemes, the patriarchy, and consumerism, which I suppose is sort of what you're picking up on here? Without capitalism etc there would be no need to transition, as gender would have much less strict roles and possibly more expressive than what we're currently allowed. However I suppose that's part of another debate.
One way of fixing these said preconceptions is, like you addressed, transitional surgeries etc. which is again like you said; expensive and complicated.
Another more radical way that may require more brain power and a little thought, is breaking down the very ideas of gender and sex. What is gender? The bits you have in your pants? Whether or not you wear makeup? Who you fuck? The line is at first sharp and hard, but the more you think about it, the more it blurs. (For me at least, I'm unsure if others feel the same around here)
Maybe the way forward here isn't so much telling trans people that they're special snowflakes, but instead recognizing that there are many individuals of many different backgrounds who feel this way, and maybe it's not the people but the boxes they are forced into that's not right?
I'm not sure if this makes the most sense, I'll come back tomorrow and expand or something maybe. I'm tired right now.