There is a split between the social, physical, emotional and sexual portions of a persons transition (or journey.) While I can not speak for every transperson, the social transition was by far the most important for me. There is a rarely noticed feedback look of 'I present female' --> 'I'm treated female' --> I feel validated and continue presenting female.

While I know of many transpeople that would love to have the surgeries, most haven't and might never be able to. This can be due to wealth, health or insurance issues. Sometimes health and age prevent a transperson from being able to take hormones, yet still find greatly enhanced satisfaction just from the social transition. The SRS surgeries (like a lot of pharmaceuticals) also tend to be much more expensive in the US, partly due to there not being many domestic places that performed them, on top of many insurance companies not covering them. A vast majority of the SRS surgeries have been performed in Thailand (a second world country) for a long time, where it is cheaper and more socially acceptable.

My point out of all of this is that the privilege of wealth and access doesn't really apply to a 1st, 2nd or 3rd world country but to the transgender community as a whole (who also have a much lower socio-economic status on average, kicked out of their homes at an early age, can be fired or kicked out of an apartment or rental with no recourse.) The entire community world wide is under-served as a whole (outside of Caitlyn Jenner) and there really isn't a privilege disparity between transgender people. The 'privilege' is a rarity in out community unfortunately.

The other point here is to look at social acceptance of the trans community to exist. It's more common for transpeople to be treated as an equal 1st and some 2nd world countries. But most 3rd world countries are very conservative and tend to shun or worse those that 'come out' as transgender.

Surgeries, while maybe preferred for some, aren't what make a transperson transgender. It's that inner feeling of how they would like to be treated (as male or female) and reciprocated by society that creates the feedback loop of gender that is more than sufficient for most.

I think I answered your question in all that. Lol