I've never used AWS so perhaps I'm mistaken, but api gateways normally provide extra functionality on top of just proxying the request. You can still set up a server listening on port 80 or 443 with a public IP and make requests to it without being charged per request.
You can, and if you want to use Lambdas, you can also route to them from ALBs, which has a bit confusing of a pricing model for comparison, but has no per-request cost.
Oh, ALBs. Now that's a mess. You'll either be charged per new connection, per concurrent connection, per byte, or per rule evaluation, depending on which is highest any given hour.
