I'm no psychologist, and this is just my own opinions formulated from thinking about this a lot, and I of course am not making light of anyone who has found themselves in a "transition/surgery or die" situation. But here's how I think about it ... if you're contemplating suicide you often have a multitude of issues that you feel you have "no way out of". Just from reading other people's posts on these forums it seems like a lot have additional mental issues to deal with on top of their gender ID, so that has to come into play. The reality, for me at least, is that there are always ways out. There are always other paths and avenues open. To me, my gender issues are not equal to terminal cancer so I never gave myself a death sentence over them.
And now that there is an option for transition and surgery (even if it's cost prohibitive for some, the option is still there) I think it does lead to more "I have to have this or I'll die" thinking. It is very easy for the human brain to convince itself of a need. Try thinking about your favorite food for a minute and I bet (especially if you're currently hungry) you're going to start feeling like you need that food ... you must have it right now! You're brain knows you can probably just go out and get that food and be enjoying that and your "problem" of wanting can be solved.
I think back to when I was younger (pre-teen to teenager) if someone offered me the option, "hey you can transition to male and live the rest of your life as male" I probably would have jumped at it. But I also made other poor and questionable decisions in that era like insisting that I was going to be an NFL football star, launching my dirt bike off a 15ft cliff, and eating 8 cupcakes in one sitting. So with the wisdom of years now in my favor, I can honestly say that I would not have given 10-20 year old me the option for a drastic, life-altering decision. While the reality remains that I was no less male then than I am now, I'm glad I wasn't given the option to change my life in ways that I could never fully go back from.
I'd also like to expand on the OPs thought and include the FTM folks throughout history. The ones I've read about did live as male. Imagine how that must have been though to have to hide breasts ... come up with explanations why you have no facial hair .... or aren't having sex with women (or can't have children) ... and to deal with bleeding every month ... and yet somehow (at least the ones we know about), did it. They lived their lives in the best manner they could. And there were societies throughout history that accepted variations of gender more than the current heavily Christian-influenced society does.
So one could argue that since now a treatment exists, why the heck wouldn't trans individuals want that? From my perspective, it's become a bit flipped around. If one takes the option NOT to transition/have surgery then their gender ID is often questioned ... especially by the "medical professionals" and other trans individuals who are taking the treatment option. Oh sure, there's therapists out there who advocate for trans individuals to go with their comfort level (and that may not include treatment), but there's also ones out there who tell their clients that they aren't trans if they don't want these things. At the other end of extremes, there's therapists who warn people that if they don't get treatment they'll end up committing suicide. So that too might add to people who have gender issues generally feeling confused and scared and that transition/surgery is the only way or they're going to die. Combine that with how segments of society treats anyone who steps outside of the norm (everything from ridicule to outright violence and the threat of death) and it's like a perfect storm for some people who are already overburdened internally with how they feel about their gender.