It might improve things a little, but it won't fix the problem. Things can't be like they used to be anymore for a number of reasons:

1)People in the past who had lots of kids were mostly low class. That is mainly because they wanted to have lots of kids helping out in the fields and farms. Also, the mortality rate was higher so people felt the need to have more kids just in case. This was somewhat beneficial for the family back then. However, with the dominance of industrial economy, families see having lots of kids as less beneficial. (It was also observable in the past that richer and noble families typically had fewer kids than lower class families)

2)People are more materialistic today. They will prefer to have only 1-2 kids and live a better life economically, than have lots of kids and live poorly.

3)Birth control won't just disappear.

The only way to have high birth rates again is to get rid of birth control somehow (maybe for religious reasons) and somehow return to a more agricultural economy.

There is no guarantee that if the sexual liberation ceased to exist the birth rates would be significantly higher in the west. Countries with very high birth rates are typically what we call third world countries.