I can't deny that I share your fears that the increased awareness of trans people could lead to vulnerable children seeing transition as a way to relieve their distress, and living to regret it. I also feel that some of the ideas that have been put forward in recent years about gender are regressive. Although some people argue it is all just down to better support and awareness, I think the change in the demographic of children presenting is not adequately explained by that alone and needs exploration. That said, I would never want to be blasé about their distress, or to rubbish their experiences because they are from a different generation than I.
I remember social media starting to come out when I was a teenager. Suddenly everyone had to have a Bebo account, where we would all obsess over how many hearts we got on our profile. People would talk on MSN and make plans for the weekend, and of course the unpopular children were never included. As someone who was bullied a lot in school, it became yet another avenue for exclusion. I can't imagine how difficult it is for children growing up now. I also feel terribly for their parents, who are stuck between trying to protect their children and not wanting their child to be left out by their peers.
I'm not sure it will ever be possible for me to provide a definitive reason for why I am as I am. I can't deny that I experienced misogyny as a child, and sadly I doubt a single girl has over grown up without encountering it to some extent. I am fortunate in terms of my family. My mother always felt very restricted by her parents' ideas surrounding how a girl should behave, and what her interests should be. She would encourage both me and my brother to pursue any interests we had. I remember that my brother loved dance as a child and she would take him to classes. My dad was definitely more 'traditional', and she recently told me that at the time he had said the classes might 'turn him gay'! That said, my dad would always ending up doing as he was told when my mum put her foot down, which she did readily 😂.
I remember sexism being more obvious outside my home. When I was young all the children on my street would play outside together nicely. However, there was one dad who started organising football and cricket tournaments. I wanted to play, as did other girls, but he'd say 'girls don't play football' and leave us out. I know that isn't an extreme example compared to the awful misogyny that some girls and women face, but I do remember it vividly as I was so angry. Slightly off topic, but I thought people would be tickled to know that my mum then organised a sports day (complete with egg and spoon race!) for all the kids on the street. Other parents were invited to run events for us, with the notable exception of that dad.
I would say that I don't think socialisation alone adequately explains my situation. I can remember distress from being very young, and though I know children begin to be socialised from birth, I don't think the developmental maturity matches the kind of thought process you have outlined. I also think it is relevant that spending time as part of the lesbian community, which really felt like a safe haven from stereotypes (both in relation to sex and sexuality), didn't improve my sex dysphoria.
Finally, I don't think it is accurate to say that I thought my life would be easier living as a trans man. Whilst I had a lot of distress about my sex, I got a lot of relief out of being a proudly gender non-conforming lesbian, and the process of meeting similar people and being involved in that community filled me with a lot of hope. However, it didn't have the effect on my ability to accept myself that I had hoped for. In contrast, I tried to suppress the feelings I had regarding my sex due to being fearful of the taboo and stigma associated with it. I know it doesn't seem like such a long time ago, but the attitudes people have today compared to when I was young feel like night and day.