Is it appropriate for assistant professors to supervise PhD students?

Isn't it wrong that an inexperienced assistant professor (who is not far from his PhD studentship days) can take control of one or several PhD students? Don't it reduce the education/research quality?

For certain institutes I've been in, I would find myself asking the opposite question: isn't it wrong for senior professors to supervise students when they have little time for them?

Of course it is not always the case that full professors have no time for their students, but I have seen it happen many times: I've seen cases where students were meeting their official full professor supervisors once a month (or less frequently) and putting names of supervisors on papers that the supervisors had never read. This seems to me to be prevalent in research institutes where the hierarchy tree has a high branching factor to get value out of available funds (few Full Professors, lots of PostDocs / Assistant Professors, even more PhD students and Research Assistants, etc.); in such cases, the priority for senior professors is getting funding for and managing projects. In my case, when I was a PostDoc in such an institute, I was doing the day-to-day supervision of a number of students whose supervisor(s) had no time for them.

Of course it varies from place to place. But my hypothesis is that by the time you reach the Assistant Professor level, either you will have the necessary skills and personality to be a good supervisor, or you will probably never have those skills.

In summary: I don't believe that seniority amongst professors is a good predictor for quality of supervision.

Isn't it wrong that an inexperienced assistant professor (who is not far from his PhD studentship days) can take control of one or several PhD students?

It is alright for an assistant professor to guide one or several doctoral students. He is not experienced in probably guiding PhD students, but, he is definitely experienced in conducting research, which will help him translate this to guidance.

Don't it reduce the education/research quality?

Well, maybe. Supervising PhD students is a learning activity like most anything else. As such, it is to be expected that maybe when an assistant professor supervises her/his first student, s/he may do things that should would handle differently later on. But this is not tied to the status of the person, but to her/his experience in advising. So if you don't let assistant professors advise PhD students, they would start doing it later on and be equally bad in it, because when would they have learned how to do it?

An additional concern is that there are only so many full professors to go around. While I concede that working with a more senior professor may have advantages, these advantages would likely disappear if every senior professor has to handle significantly more students (as the entire 'advising force' of assistant professors falls away).

I should also add that, in general, assistant professors are not nearly as inexperienced as you seem to assume. Today, at least in my field (CS), there is hardly any assistant professor that did not have multiple years of postdoc experience, which also includes co-supervising master and PhD students. As such, I am not sure if the problem you seem to consider even exists.

Edit based on ff524's comment:

I think the question intends to ask, "Is it appropriate for assistant professors to supervise PhD students alone?" In some places, PhD students working with an inexperienced advisor are also co-advised by another (more experienced) advisor.

Yes, this is actually the case in many well-respected university (dutch universities come to mind right now). I think this is great if the main responsibility/load is still on the junior professor, with the senior person being more an advisor to the advisor than to the student. If the model degenerates into the junior professor basically being a proxy for the senior person, this seems counter-productive.

Of course it's appropriate. In many research-intensive academic departments it's the assistant professors (the younger researchers) that are doing the innovative research.

I had several friends who worked with an assistant professor years ago. That professor later won a Nobel Prize for the work being done in his assistant professor days, with the help of those students.