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?
No, it is not wrong.
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.