You are right. But there are some other factors:
In Soviet Union there was a state policy: The university education is free. If your grades are high enough you even obtain some scholarship money. But after you graduate there is a procedure of "distribution": There is a list of employers pretending to employ the graduates, and the graduates choose the employers. The distribution begins from the best students which can choose the best employers, and then the worst students choose the rest. Then, the employer must give the new worker some place to live and spend efforts for his specialization but the worker must work here 3 years as a payment for his education.
The other state policy was that it was almost impossible to buy an apartment (cooperation and private sector aside). Instead, there was lot of state and employer's place to live rented for the nominal fee - but as a rule with a terribly long waiting list.
And this week I've read somewhere the article stating that the free education and free place to live are necessary to prevent the condition "poor became poorer, rich become richer" and the resulting crash of the society.
Now let's return to the procreation. In Soviet Union there was enough place to family life and enough time for family life. ("In USSR there is no sex" is a famous phrase I personally heard from TV). In USA (and in modern Russia too) you either have no place or no time for procreation since your student loans eat all your free money and correspondingly all your free time which you spend to earn money.
And the second factor is that in USSR your wealth didn't count, you needed something else for girls' attention. Creativity, for instance. Ability to obtain USA jeans. Or CPSU membership :-)