Yes, I read the Daily Mail links.
What jumps out at me is that you have an "expert" proclaiming that this procedure may be performed on men in the next 5-10 years, followed by the rest of the article explaining how risky and complicated this surgery is when performed on women.
In the first article linked to, Dr Paige Porrett is quoted as saying this could be performed on men soon, but the rest of the article says absolutely nothing about how that would happen. It describes how it works on women, in ways which obviously do not apply to men. For example, when it talks about how a woman receiving a transplanted uterus will then typically begin to menstruate. Trans women cannot ever menstruate, because in order to menstruate you need to be ovulating. There is no mention of ovaries forming part of the transplant; indeed, it is expressly stated that women who have received a transplanted uterus become pregnant via IVF. So a theoretical man receiving a transplanted uterus would not receive ovaries, not ovulate, and not menstruate. They could probably simulate menstruation by taking the combined pill. However, that would probably be quite dangerous because the vagina is self cleaning whereas a "neo vagina" is not. Deliberately causing bleeding in an organ which needs to be manually cleaned seems like it would pose an infection risk.
The article says nothing about a male recipient actually being able to get pregnant and give birth, which is of course the sole purpose of a uterus transplant. They are only performed on women for the purpose of giving the recipient the opportunity to bear children, and are removed after she has finished attempting pregnancy so that she can stop taking the immune suppressing drugs which stop her body from rejecting the organ.
There are many reasons to suppose that a transplant into a male recipient would be unlikely to be successful, for example, the fact that the male recipient's blood vessels would be bigger than the blood vessels in the transplanted uterus, making it much more difficult to join the transplanted uterus to the male body, reducing the chances of success and increasing the risk of life threatening blood clots.
This is important for two reasons. Firstly, it suggests that receiving a transplanted uterus is highly risky for the male patient. (Indeed, the only time it has ever been attempted, the patient died.) It is difficult to see how the patient's doctors could sanction a transplant which is not done to save their patient's life (as all other organ transplants are intended to do) and which might well kill them. And secondly, if there is a shortage of uteruses available for transplant, the uteruses which are available should be offered to the most compatible recipient, meaning the person whose body is least likely to reject the organ and most likely to achieve a successful pregnancy. Given that the donor organs come from dead women aged 18-40 who have previously borne children of their own, I can't imagine there are that many knocking around, and there are a lot of women with absolute uterine factor infertility who have a much better chance of a successful transplant and would be considered a priority. It's hard to see how any male potential recipient would ever make it to the top of the waiting list. And it does bear repeating that the uteruses preferred by the University of Ohio come from dead women aged 18-40 who have previously borne children. In other words they come from the dead mothers of minor children. It seems pretty disrespectful to their memory to waste their uteruses on unsuitable recipients whose bodies will most likely reject them.
Finally, even on women this is a hugely risky procedure. Any resulting babies are born by C-section because doctors don't know whether the mother's (natural) vagina is capable of childbirth, even though the baby would fit through her pelvis. (A baby will not fit through a male pelvis.) Transplants are not currently performed on women over 40 due to the increased risks of pregnancy in older mothers. Let's take a moment to think about that. They won't transplant a uterus into a 41 year old woman because it is considered too risky. But they'll transplant one into a man within 5-10 years? Pull the other one.
Then even if a male recipient did undergo IVF and manage to achieve pregnancy in the transplanted uterus, which I HIGHLY doubt, what about the risks to the baby? This has never been done before. We have absolutely no idea what unexpected effects a pregnancy might cause in a male body. It is simply unethical to use a human embryo as a guinea pig in this sort of experiment. Just one example: infections in the vagina and cervix can cause very serious pregnancy complications and in severe cases cause the woman to lose the pregnancy. One of the arguments against having sweeps at the end of pregnancy is the infection risk. Even a doctor or midwife putting their gloved fingers inside the woman's vagina to check the cervix increases the risk of infection. Now imagine that cervix is at the end of a neo vagina which doesn't self clean and requires daily douching.
Honestly, there are so, so many reasons why this is unlikely to ever work, and any doctor talking about how complicated and risky this surgery is in women and then claiming that within 10 years they'll be able to successfully perform it on a man is talking out of their arse IMO.