This is incompatible with TCP/IP networking. In TCP connections, (sender_address, sender_port, receiver_address, receiver_port) is a unique combination. Those numbers together uniquely identify the sender talking to the receiver. For a public webserver:

* sender_address is the client machine's IP address

* sender_port is a random number from 0..65535 (not quite, but let's pretend)

* receiver_address is the webserver's IP address

* receiver_port is 443

That means it'd be impossible for one client IP to be connected to one server IP more than 65535 times. Sounds like a lot, right?

* sender_address is the outbound NAT at an office with 10,000 employees

Now each user can have at most 6.5 connections on average to the same webserver. That's probably not an issue, as long as the site isn't a major news org and nothing critical is happening. Now given your scheme:

* receiver_address is the gateway shared by 10000 websites

Now each user can have at most 6.5 connections to all of those 10000 websites combined, at once, total, period. Or put another way, 100,000,000 client/website combos would have to fit into the same 65535 possible sender_ports. Hope you don't plan on checking your webmail and buying airline tickets at the same time.

Not all workloads are HTTP.

> gateway .. for millions of customers

That's basically what an AWS ALB is. It's not provisioning bespoke infrastructure when you create it.. it's just a routing rule in their shared infra.

If Amazon wanted, they could easily have shared IP's but the cost of an IPv4 isn't so great that this approach has been warranted yet, clearly.