Sort of, but also sort of not. I mean yes, lots of parents are like this, for a variety of reasons. No, this isn't unique to just parents of Millennials and Gen Z. I would argue it's probably massively more common for older generations.
In terms of US culture, I would say that you're noticing that Gen X is really where things started to materially change in major ways that makes not having kids a more socially and physically viable option for a lot more people. To a lesser extent, these changes are also seen on a global scale or had global impacts.
To use my own parents as an example, they were born in 68 and 69, and would've been the first generation to grow up with some of these things and/or seen these changes.
The FDA approved the Hormonal Birth Control Pill for women (1960).
In 1965, the Supreme Court decision of Griswold v. Connecticut (Griswold) finally and completely rolled back state and local laws that had outlawed the use of contraception by married couples. [Wikipedia says: "France repealed its anti-birth control laws in 1967. Similar laws in Italy were declared unconstitutional in 1971. In Ireland, legal condom sales (only to people over 18, and only in clinics and pharmacies) were allowed for the first time in 1978. (All restrictions on Irish condom sales were lifted in 1993.)" ]
The AIDs crisis in the 1980's also increased the availability of free condoms, and national campaigns for condom use took place in the US and Europe in 1985-1987. Condoms were also pushed in other countries as both a health measure (minimize or prevent STIs!) and also for imperialist reasons (eugenics. It was to help "solve overpopulation" in poor non-white countries).
This rise in condom campaigns is what got them to be introduced to big stores in the US like Walmart.
Advertising condoms on TV in the US was still illegal in 30 states by 1975.
The 60's and 70's is actually when US condom production regulations were tightened, making them more likely to be reliable and effective as contraceptives.
While women had the right to open bank accounts in the 1960's, it wasn't until The Equal Opportunity Credit Act of 1974 was passed that American women were guaranteed the right to open checking accounts and credit cards solely in their own name (without needing the signing permission of their husband or father). (I've seen claims the UK guaranteed this right in 1975, but I don't know the source for that.)
Before it was overturned, Roe v. Wade was decided in 1973, and led to abortion access improving.
Using my mom as context, she was about 17 in 1985. All of this shit was brand new.
Put simply, Gen X is really the first generation to even have relatively common access to reliable forms of birth control (like condoms in regular supermarkets, or freely passed out at health clinics) and where women could manage their own finances (thereby skipping the financial need for marriage) and receive employment protections (I skipped listing dates of acts that protected women from sex/gender based discrimination in the workplace, but those are also relevant).
And all the meanwhile, (in the US) they grew up in the Reagan purity culture abstinence only era, chockablock full of evangelical fundies who try at every turn to make things like contraceptives, abortion, and sex education impossible both to access and highly demonized. (That's how we get shit like the quiverfull movement.)
So anyone pre-Gen X? Had FAR less opportunities to avoid having children if they didn't want them.
That Gen X still had kids even if they didn't want them or only wanted the idea of them is indicative of: 1) the relatively recent social changes still shifting cultural norms as they became adults 2) relatively recent protections and accesses that allowed people the option to not have kids, meaning being a parent was only then becoming an active choice of desire for many people! 3) generally the tension between parent-child and identity formation across time always existing.
Basically this was the first generation where you could more easily actively choose to avoid having children (although stigma still exists, it was becoming easier) and likewise actively choose to want to be a parent instead of it just being an expectation and often inevitability of life. And you don't (probably often can't) develop reasonable expectations of children as unique individuals if you have little/less choice in the matter of them happening to you.
To so many people, their ability to consider children wasn't framed as "do you want to raise small humans?" But "you will end up with small humans to raise, so how will you deal with that in your life?" and then they developed coping mechanisms to try and find personal satisfaction in a situation where agency was not guaranteed, and those were often terrible for everyone.
The very notion of family planning as an active choice, reliable, accessible, and consistent contraceptives, safe abortions, being able to remain unmarried as a woman but still have equal rights, contraceptives being legally allowed for married people — all of this is really recent to Gen X parents, and only a little less so to Xennials. Frankly before that people weren't really given many options and people weren't really asking if you wanted any of these things.