Wouldn't the real cause of the depressed birthrates be the requirement to own a car in order to have children? If you aren't a slave to your vehicle there's no problem with the available space for car seats.
That said, have 3 kids aged within 5 years of one another and we never had to get a double buggy. The older ones would be OK to walk (3 year olds will walk a pretty long way if you're patient) by the time the youngest got too big to be sling-carried.
It comes down to, dealing with three under-5's single-handed while out and about is pretty hectic full stop. Most places with high birth rates "solve" this by not allowing mums the expectation to be away from the house much, and/or they're multigenerational households where grandma or an aunt can be home with some of the kids.
So to your point, I think it's less the requirement to own a car, more the expectation of a kind of lifestyle which often, though not always, in turn requires one. Childcare for 2 year olds here is often upwards of $2500/month, now that's a contraceptive.
I would also add as a car slave that the kinds of cars large enough to fit the kinds of car seats marketed in the US are tens of thousands more than a compact or mid-size sedan, and that in a mid-size sedan having a car seat in the rear-facing configuration significantly constrains how far back you can put the passenger or driver seat. This is true even for the narrower seats that are designed for three-across seating. And worse, you might not have the latch system or an appropriate kind of seat belt on that third seat.
Or you're one of the millions of people who live in developing countries which have low cost of living and low housing costs. Coincidentally this group has very high birth rates.
The alternative - small, crowded population centres where everyone knows everyone and three, even four generations live in the same household can of course be limiting, even suffocating.
But there's a reason why, for all that the 1950s autonomous nuclear family is held up as some kind of ideal by tradwife fetishists, it's also the milieu in which Valium and sleeping pills became popularised.
Where in the USA do you live where I can support my wife and kids on one income? We'll move immediately.
There are plenty of places that can be afforded on a single income if you work in tech and can work remotely.
Examples: https://www.zillow.com/homedetails/10-Regina-Dr-Paris-IL-619... https://www.zillow.com/homedetails/804-N-Walnut-St-Pontiac-I...
So a three-bedroom apartment might not be enough if you have three kids.
It's not that you can't, it's just that it's not the standard of living most western people expect.
My mother - I found out years after I'd left home - was worried that I resented the fact I had a small bedroom while my younger sister got a larger one - but in reality I didn't care at all, she's an artist, she makes stuff which actually exists, of course she needs space; I write software, which conveniently takes up no space, whereas if I'd had to share with her that would be extremely problematic and wouldn't have gone well. I could be in my tiny room and that was enough.
I grew up privileged and had my own space, but a shared space between siblings was normalized. But going into high school with that constraint, it seems stifling. I really have to wonder what effects that lack of privacy / autonomy has on a developing mind. There are probably studies but it's not something I'm about to research.
> If you aren't a slave to your vehicle there's no problem with the available space for car seats.
The abstract says the effect is limited to households with a car.
Yes. The one-time setup costs for "properly" raising kids are probably around $30k. All the kids stuff is extra expensive (in the west) and for the kids seats you need a large car (in the west) and there's social stigma against kids sharing a room (in the west), so you also need a larger apartment.
The real money goes to:
1) Healthcare (in the US).
2) Childcare or foregone wages.
3) School/housing location (same thing; either tuition, or spending 20+% more for the same amount & quality of house in a nicer school district [and the ongoing cost of servicing the extra mortgage on that]; you can skip this, but if you can at all afford it, you'll not feel like it's optional)
4) Space. Larger housing and larger cars. You can skip this kind of (larger car is less-optional if you have more than three kids) but at significant cost to QOL.
Wrangling 3 or more toddler and up kids in public can be hectic.