I do not think the current level of children in Japan will be constant to 3100. Looking at the steps in the demographic transition each step is at most a couple of generations.

(See Wikipedia for mre about that graph.)

I see no reason why stage 5 would be an end stage, it seems more likely that decreasing birth rates for a couple of generations will trigger some societal changes that changes the birth rates (assuming a lack of external changes). So I do not think Italians or Japanese will disappear, but I do think their societies will change. Thinking about how might be interesting, the population will grow older and - assuming the difference in life spans between men and women does not go away - thus more female. How will that effect their cultures?

If the low number of children is considered a problem, the nordic countries has shown that greater equality and lower burdens on parents does increase the number of children. Paid parental leave, heavily subsidized day care, free health care for children, paid leave for parents when their child is sick and so on. If more governments see themselves forced to adopt such measures, then that might have positive effects on their politics in general.

Btw, if someone inherits Italy it would (demographically) more likely be people from Africa, then from eastern Europe or Middle East. Here is a map of fertility rates in different countries:

(found at Wikipedia)

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