No, no, no. That is a misconception and it makes me angry every time I hear it. There is no data one way or the other that suggests that T leads to any kind of issue that would necessitate a hysterectomy. Most guys experience some atrophy of those internal organs that would be removed in a hysterectomy. But that typically isn't something that you would feel or even know about unless there were other issues.
But anyway, no. I know quite a few guys who have been on T for years with no hysterectomy. Some people get one because shark week reappears on occasion. Some people just don't like knowing that stuff is there. Some people get one because it's required for other bottom surgery procedures. If it isn't bothering you and you don't have a need to get it out, then there is no issue with it all staying in. One thing to be mindful of is that you would need to continue having regular gynecological exams if you didn't have one. Some guys see a lot of benefit in getting one strictly for that reason.