Birth control + abortion + IVF are what makes fertility rates a choice for those with the wealth + health to choose them, but like you (I think) I wouldn't actually call the existence of the choice the root cause of declining fertility. Instead, the lack of choice covered up the fact that many people would not choose to have children in our society, which is the root cause of falling fertility rates and a failure of our society. As well, there is structural bias against the choice to have children, because birth control is extremely cheap & accessible compared to IVF - if we imagined a population overall neutral on having children, the higher availability of birth control compared to fertility increasing treatments would bias it towards less children anyway, the same way that a tax on cigarettes leads to less people smoking.
Why don't people choose to have children? Part of it is cultural, aggressively anti-child beliefs. A big part of it in my generation is depression about the future - many people feel the future is hopeless because the government is not doing enough about climate change and we seem to be getting closer and closer to a large war. Most of my friends would express that sentiment when asked why they don't want children. A big part of it is financial & health related - a lot of people don't feel comfortable having children unless they are in perfect health & quite wealthy, because of proto-eugenicist ideas that are just accepted as part of our culture. Some of this is individually rational choices: if no one will provide you with appropriate financial & medical support for the full-time, critical-to-society job of raising children, some people accurately believe their standard of living will drop dramatically if they have a(nother) child.
All of these issues can be solved. The government can act on climate change and de-escalate tensions rather than preparing for war in order to let people have hope for the future again. The government can make IVF and other fertility increasing treatments free to the end user and otherwise as accessible as possible to lower the barrier to entry as much as possible. The government can choose to compensate people for the critical-to-society job of making & raising children, ensuring that having children is not a financial burden compared to not having children, & structure healthcare + educational outcomes such that people do not feel they and their children's lives will be worse after having a child, or at least that that isn't a true statement in terms of personal standards of living.
Western governments choose not to do these things because they don't need to, because they can rely on other countries having widespread lack of choice + poverty & instability to push young people to emigrate to the West & keep Western demographics very healthy. This solution works (at the expense of poorer countries), and while it can't last forever it can last for a very long time from our perspective. Eventually though, countries will need to solve the fundamental problem or accept widespread decreases in wealth & standards of living as population decreases.