I have four kids. I have a very good income, my wife works part time, we own own a nice house with a yard (that has probably tripled or quadruple in cost since we bought it...adding another wrinkle to the mix), my kids attend public schools (both charter and traditional), and we live in an area that, at least until recently, has been lower cost. It's still not easy!
My wife and I got started with our family later than some but earlier than many--after grad school and a couple of years in full-time employment but still in our 20s. It would be much harder had we waited until our 30s to start having kids.
There's immense pressure to have all of your kids participate in sports, clubs, tutoring, music, etc. Many of these are very costly. My kids are mostly a chip off the 'ole block and suck at sports, so that's been a big time and expense saver, but for kids who participate in higher levels of athletics, even at the middle school level, you are looking at multiple thousands of dollars per year per sport per kid and many, many hours per week. It's crazy! Toss on piano lessons, summer camps, daycare/childcare if needed, and all the "extras" add up very, very fast.
Add up preschool and K-12 private schools, which many people feel they must, and you can be paying 15k - 40k per kid per year.
A couple of years ago we were on a family trip to Boston and we popped into a coffee shop. A woman came up to me and said "Three kids?! Wow, it's like the old days. How do you afford that? Are you a crypto bro?" (I am not!)
Similarly, we were on a trip to Italy and multiple people--probably at least 10 over the course of a week--came up to us and said something along the lines of "It's so great to see a big family. I was part of a big family. I would love to have more kids [or any kids at all] but it is so expensive!"
My wife and I both knew we wanted kids and we're very family oriented. Giving up socializing, going out drinking, going to costly sports and other events, was not a problem for us! We also have family nearby, which is another lifesaver. If we didn't have the money, the family, and most importantly the desire, we never would have been able to have a large family.
I completely agree with you regarding subsidies. It takes a lot to move the needle. A thousand bucks here or there is just not going to move the needle.