So I was CTO of a bootrapped startup (10s of millions ARR ) growing approx 70% YOY, likely a unicorn but never discussed on HN.
What I would say is the argument isn't false, but the assumptions often are.
You will for example have diminishing returns on the CaC. Spending more will make the number go up usually.
This explains why you wouldn't just spend it all year 1 and refinance.
Finance is indeed more expensive, and black swan events can cause mass churn, this why pulling out costs might sound good on paper, but in reality could potentially screw yourself over.
Indeed the payback of the customer needs to be short enough to validate profit. The longer it is, the more likely one of those black swan events will distrupt lifetime.
But I suspect there's more businesses out there doing this that are discussed here.