Those are good points and I think we agree. No one can choose their gender, and saying that trans people can do that is offensive. (And worse, it can fuel the horrible "if you can choose your gender it means it's just a phase, go to the shrink and you'll soon feel better about the gender God chose for you" thing.)
As for whether or not people internalize their male privilege, would you agree with me if I said that I believe it relies on the person?
A person that is able to transition early obviously has a different experience than those who try to live as the wrong gender, because it's expected of them, and then forty years later they finally come out to their families. The latter is going to cling to gender roles because they believe they have no choice, and is scared of being found out. They might also subconsciously internalize a lot of harmful patriarchal ideas (just like cis women and men do when they're raised in conservative families). Whereas someone who transitions early will be met with transphobic awfulness at unexpected turns, and not really get to benefit from, say, male privilege because this society is openly hostile to people who doesn't fit into the binary.
But both of these people will have been trans all along, and they have both been hurt by transphobic attitudes in their lives, no matter how early they transition. If we're going to talk about privilege and oppression, it's really important to keep that in mind and not just focus on whether they have male privilege or not.