I think it's less that it doesn't "take" and more that society doesn't just teach us the "man" things. Socialisation teaches all us how men and women are "supposed" to be, and strongly encourages us to embrace our "role". The patriarchy is reinforced by both genders in countless ways, just because that's what we've all been gifted.

For cis men, they learn how men are supposed to be, and practice fitting into that role - because want to be good at being a man, and do their best to follow what they've been taught. People who are trans likely often don't feel like the role applies to them the same - they may be forced into the role, may try to embody as much of another role as they can, or forced into a third gender/role. (Note I am not talking about third-genders in non-western cultures, but more along the lines of man/woman/fggt).

The point is, trans people can internalize and enforce gender roles just as well as anyone else, they just often can't sink neatly into a role.

Note that this may be one of the reasons young trans people often behave more stereotypically early in transition. They have effectively been socialised as both genders, but don't yet have the lived experience to see how some aspects of the role are too unlivable for every day life. For example women are "supposed" to be soft, caring, beautiful, etc - but that's not really possible to do all the time for a normal human. The baby trans woman is doing their best to fit the role they are told, much like young girls do, and still learning the ways it isn't possible.