By default a NGW is limited to 5Gbps https://docs.aws.amazon.com/vpc/latest/userguide/nat-gateway...
A GB transferred through a NGW is billed 0.05 USD
So, at continuous max transfer speed, it would take almost 9 hours to reach $1000
Assuming a setup in multi-AZ with three AZs, it's still 3 hours if you have messed so much that you can manage to max your three NGWs
I get your point but the scale is a bit more nuanced than "thousands and thousands of dollars on your bill in less than an hour"
The default limitations won't allow this.