[ECS] [request]: Alternative to expensive NatGateway in private subnet

**Tell us about your request**

Whenever you need a container to access the internet from a private subnet, you need a NatGateway. PrivateLink does a decent job of removing the need to do so in some cases (like ECR access), but in a connected world, the need for internet access remains high. A NatGateway, especially when using more than 1 AZ, is really quite expensive however. It also consumes an ElasticIP, even when I don't care for a static IP, which causes me to hit service limits. This must be such a common pattern, that I'm wondering if an optimized and cheaper alternative to NAT Gateway for ECS private subnets cannot be found.

**Which service(s) is this request for?**

Fargate, ECS

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**

Not hard, just a big portion of the monthly bill, for such limited business value.

**Are you currently working around this issue?**

No

**Additional context**

**Attachments**

No repository files, tests, or entry points are identified. Start by reviewing the request's NAT Gateway, PrivateLink, Fargate, and ECS constraints, then determine whether a cheaper alternative for private-subnet internet access can be specified. Done requires a concrete, validated proposal rather than a small code change.

Written by the indexing model from the issue text.