Have more children to even out the population pyramid?

What? Take the example of a country with 3 old people, 5 adults and 2 children. The government has to pay pensions for 3 and expensive healthcare for 2 (vaccines, pediatrics, etc).

If the adults have more children, we'll have the same 3 old people, the same 5 adults and 3 children. This means one more pediatrist, thus increasing costs.
If the population stays as it is, nothing will change.

Why do the governments of countries with aging populations encourage childbearing? They're not magically displacing the elderly, they're simply introducing a new expenditure. It makes sense if you don't want your country to die, but Japan and China are examples of this and they aren't dying any soon.

It makes sense if you want to keep your country from dying, but this reason is never cited and instead they cite the need to "even out the population pyramid because old people are too expensive to maintain". This doesn't make any sense.

People need to learn acceptance of death, and end their lives when the time comes, to free the space for those who come after them.

But they won't, because most people are egotistical pieces of shit bent on prolonging their physical life beyond all sense and reason. People are pieces of shit that would rather live their lives in pain, being constantly sick and near-mindless, than care about the younger generations.