$1k per week is very high even for the SF Bay Area or Manhattan.
I would need proof to believe it, and am interested in what kind of pampered existence these kids have at school considering TN’s average CoL, and even if such a daycare exists, it is surely not representative of 99% of daycares.
I mean, I'm not gonna give you the proof there as this is as anonymous an account as I can be.
One thing would be to try to look at the wait lists of various daycares. My buddies in TN are at ~3 years. We were at ~1.5 years. And yes, it's quite common in the US for the waitlist for a daycare to be longer than 40 weeks of human gestation.
Daycare in the US in general is really not very well tied to the local CoL. Many factors influence the cost and CoL is but one. Things like the quality of churches really affect things in ways that other services are not affected by normally.
In general, if there is a waitlist, then capitalism has failed. You'd just raise prices until there is no more waitlist. But with daycare, you can't really do that without knocking out a large percentage of the workforce. Hence waitlists.
NPR has a good PlanetMoney episode from a while back on the issues with daycare in the US. It's worth checking out.