First off, API Gateway might not have been the best choice here; an ALB would probably do the trick for this use case and be cheaper. Debatable if it's fair to include API Gateway in the cost anyway; Lambda is really the "serverless" bit here, but I guess Lambda by itself isn't all that useful if you have no way of invoking it.
Beyond that, they're pushing "slower and more expensive" as a sort of indictment of serverless, that it's worthless. It's a trade off. You're trading price and performance for someone else managing the infrastructure for you. For some people that might be a reasonable trade off, and for others it might not.
Put another way: serverless is more expensive than EC2 -> EC2 is more expensive than a dedicated server -> a dedicated server is more expensive than buying your own and racking it -> etc.
Well, yeah, that's only all true if you only consider the narrow band of cost that you've cherry-picked to be relevant. Obviously buying your own server and racking it has other costs than just the server and the colo space, managing an EC2 instance costs more than just the per-hour rate AWS charges, and so on.