No. Birthrates have been dropping, but this makes getting pregnant less predictable. There are other forces at work reducing the birthrate, and I think those would be enough without complicating people's lives.
I would say the biggest issue with declining birth rates are social and psychological in nature and NOT physiological. People simply work too much, for just one example.
I'm inclined to agree with you, despite everybody else seeming to fundamentally disagree. I'm not convinced by either of the arguments in response to your comment. We have huge amounts of unemployment in the west and an economy that is tending towards more automation and fewer jobs for humans, so why would a decrease in the size of the labour force matter?
It's clear that people will continue to live longer and that birth rates will continue to fall, either by necessity (overpopulation) or due to factors like this. I hold the view that far too many people unnecessarily have children due to societal norms, family pressure, a bizarre and slightly narcissistic desire to have their genes passed down to future generations (adoption is incredibly important.) Obviously I'm not saying having children is wrong, just far too many people see it as a necessary part of their life when it really shouldn't be. Having children is an inherently selfish decision and unless you're prepared to sacrifice a huge amount of freedom to afford your children the best upbringing, then maybe having children isn't for you.
Maybe I have too much faith in modern medicine (I doubt it, modern medicine is incredible) but I fully believe a trend of dropping sperm count is not apocalyptic. It'll probably result in benefits such as fewer undesired pregnancies. The important thing is to ensure that people of any economic status have access to fertility clinics, and for IVF and related procedures to not be cost prohibitive for non-wealthy people.