1000 lambdas with 1000 database connections is also going to be a horrible way to do things on the backend. Add in the cost of RDS proxy for lambda and the ECS solution becomes even better.
I personally don’t think running on EC2 is particularly difficult to manage, and it’s even cheaper again.
So yes, very expensive fast if you get much traffic at all. That c6g.large should easily be able to handle dozens (if not hundreds) of requests in parallel, especially if many of those requests are going to have to wait for results from a database.
If you have more than ~800 hours of Lambda execution time per month (30 days being 720 hours), then you're better off with the c6g.large. The only reason to choose the Lambda is if your traffic is extremely bursty and the c6g.large can't handle the load.
Of course, this is all assuming you're using a 1 GB Lambda. Likely, your Lambda needs less, in which case the amount of traffic needed to make the EC2 more worthwhile higher.
If you want to compare AWS Lambda with EC2, you need to bring in AWS Load Balancer, Auto Scaling, Security Upgrades for the OS, Healthcheck and many more.
Yes, Lambda is not needed in a lot of context, but if you have the expertise to use it and you want to provide enterprise-grade compliance, it's a walk in the park.
Bringing the long-lived server back also makes things like long-lived connections, memory caching, cold starts and database connections a non-issue again.
The costs certainly are not as cut-and-dry as I originally expressed it.
[0] https://docs.aws.amazon.com/lambda/latest/dg/gettingstarted-...
This has been scaling really well for us and affordability wise it makes the development and testing phase basically free, with the final deployed costs almost never exceeding double digits monthly. This is for multi-az + multi-region deployments too.