How? Assuming both same lifestyle and same income, one need to spend money on bringing up children versus one that does not need?
When lifestyle and income all equals, DINK is definitely financially more well off than non DINK. Convince me if it is not.
Yes, money can be save. Having your kids to take care of you, is not 100%. That's why we have DINK.
However no kid, confirm 100% won't have kid take care, no doubt. I'm saying with money, you can have someone else take care and replacing this needs too.
DINK or no DINK, the probability of dying alone is almost the same nowadays, unless you're selfish enough to force your kids to take care and stay with you 24/7. If you scare of this, go old folks home, you won't die alone. DINK can also have niece or nephew to take care, if you put carrot (will inheritance) that they will get the money only if performing 24/7 duties and they die on your bed-side, likely they will do it if the money is huge. If you non DINK, likely you die off with less money to dangle to attractive (unless you rich or high income). But I suggest you old, just stay in old folks home since your main concern is dying alone.
Kid is not the solution of dying alone, you don't drag them down, you don't make them die together or destroy their long years of life to take care of you, dying person. As a parent, I wouldn't want to add burden to my children. We should have kid only if you find joy, to upbringing one, which DINK do not find it as a joy to. We should not let our own children to be an retirement product, or a by-product to take care of us when we're old.
Anyway, when we leave this world we don't even get to feel or care so much. We enter and leave the world with nothing. So what's your worry?