This is a huge number compared to the competition, but also a rounding error when it comes to the monthly infrastructure spend expenses of Amazon's target market here.
I mean, to be fair, that's a really reasonable price for a HA cluster. If you ignore the pricing models of literally all of the competitors' offerings.
You can have a Kubernetes cluster for about $15/mo for your personal project on GKE, if you can cope with several f1-micro or a single g1-small instance hosting your workloads. That's the cost of the nodes, and that's the all-in price. Prices scale up linearly for greater capacity, just add more nodes. (Then of course I guess networking, traffic, and additional storage can also add to the costs...)
If you are comfortable with Kubernetes, you should not be priced out of the market, even for hobbyist projects; the ecosystem is too valuable. I keep saying that Amazon really does not want their customers to use Kubernetes, and it shows in their market offerings. Only Amazon charges this premium for managed clusters, and they don't even seem to recommend using it in the keynote talks I've heard mentioning EKS. "Unless you know you need Kubernetes" is a great way to stop the discussion about adopting new tech.
If you are not already comfortable with Kubernetes, then the primary obstacle to your using K8S is that. The cluster pricing issue is a problem for people who are hyper-focused on Amazon, only.
If you want to use your worker nodes as load balancers via Ingress, to do this on the super cheap without provisioning any Load Balancers, then you can also do that. (FWIW, DigitalOcean charges for load balancers too, and you can avoid spending on using them in the same ways. I think they are cheaper though...)
The thing to look up is nginx-ingress settings for DaemonSet and HostNetwork mode. The settings to use might be slightly different on GKE. I can give you the one-liner I use to make it work on DO/Kops, here:
That last setting about NodePort may be extraneous, I think you can skip it... actually now come to think of it, I think that is the part that prevents the ingress from provisioning a Load Balancer in front of itself.
Note of course, that there is a reason why (it is the default and) you may be inclined to purchase a load balancer, as doing it this way is fairly likely to turn out to be not only less reliable, but also super inconvenient in a lot of ways. Not "nasal demons" inconvenient, but...